Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-09T19:52:03.566Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  05 September 2015

Yong-Geun Oh
Affiliation:
Pohang University of Science and Technology, Republic of Korea
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2015

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[Aa91] Aarnes, J. F., Quasi-states and quasi-measures, Adv. Math. 86 (1991), 41–67.Google Scholar
[Ab08] Abouzaid, M., On the Fukaya categories of higher genus surfaces, Adv. Math. 217 (2008), no. 3, 1192–1235.Google Scholar
[Ab12] Abouzaid, M., Framed bordism and Lagrangian embeddings of exotic spheres, Ann. Math. (2) 175 (2012), no. 1, 71–185.Google Scholar
[Ab14] Abouzaid, M., Family Floer cohomology and mirror symmetry, preprint, arXiv:1404.2659.
[AbS10] Abouzaid, M., Seidel, P., An open string analogue of Viterbo functoriality, Geom. Topol. 14 (2010), 627–718.Google Scholar
[AMR88] Abraham, R., Marsden, J., Ratiu, T., Manifolds, Tensor Analysis, and Applications, 2nd edn., Applied Mathematical Sciences, 75. Springer-Verlag, New York, 1988.
[ADN59] Agmon, S., Douglas, A., Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Commun. Pure Appl. Math. 12 (1959) 623–727.Google Scholar
[ADN64] Agmon, S., Douglas, A., Nirenberg, L., Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II, Commun. Pure Appl. Math. 17 (1964), 35–92.Google Scholar
[AF08] Albers, P., Frauenfelder, U., A nondisplaceable Lagrangian torus in T*S 2, Commun. Pure Appl. Math. 61 (2008), no. 8, 1046–1051.Google Scholar
[AS53] Ambrose, W., Singer, I. M., A theorem on holonomy, Trans. Amer. Math. Soc. 75 (1953), 428–443.Google Scholar
[Ar65] Arnol'd, V. I., Sur une propriété topologique des applications globalement canoniques de la mécanique classique, C. R. Acad. Sci. Paris 261 (1965), 3719–3722.Google Scholar
[Ar67] Arnol'd, V. I., On a characteristic class entering the quantizations. Funct. Anal. Appl. 1 (1967), 1–14.Google Scholar
[Ar89] Arnol'd, V. I., Mathematical Methods of Classical Mechanics, GTM 60, 2nd edn., Springer-Verlag, New York, 1989.
[Aro57] Aronszajn, N., A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl. 36 (1957), 235–249.Google Scholar
[APS75] Atiyah, M. F., Patodi, V. K., Singer, I. M., Spectral asymmetry and Riemannian geometry. II, Math. Proc. Cambridge Philos. Soc. 78 (1975), no. 3, 405–432.Google Scholar
[Au88] Audin, M., Fibrés normaux d'immersions en dimension double, points doubles d'immersions lagrangiennes et plongements totalement réels, Comment. Math. Helv. 63 (1988), 593–623.Google Scholar
[AD14] Audin, M., Damian, M., Morse Theory and Floer Homology, Translated from the 2010 French original Théorie de Morse et Homologie de Floer by Reinie Ern. Universitext. Springer, London; EDP Sciences, Les Ulis, 2014.
[Ba78] Banyaga, A., Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Comment Math. Helv. 53 (1978), 174–227.Google Scholar
[Be97] Behrend, K., Gromov–Witten invariants in algebraic geometry. Invent. Math. 127 (1997), no. 3, 601–617.Google Scholar
[BF97] Behrend, K., Fantechi, B., The intrinsic normal cone, Invent. Math. 128 (1997), no. 1, 45–88.Google Scholar
[Bn82] Benci, V., On critical point theory for indefinite functionals in the presence of symmetries, Trans. Amer. Math. Soc. 274 (1982), 533–572.Google Scholar
[BnR79] Benci, V., Rabinowitz, P., Critical point theorems for indefinite functionals, Invent. Math. 52 (1979), 241–273.Google Scholar
[BzC95] Betz, M., Cohen, R., Graph moduli spaces and cohomology operations, Turkish J. Math. 18 (1995), 23–41.Google Scholar
[BP94] Bialy, M., Polterovich, L., Geodesics of Hofer's metric on the group of Hamiltonian diffeomorphisms, Duke Math. J. 76 (1994), 273–292.Google Scholar
[BCi02] Biran, P., Cieliebak, K., Lagrangian embeddings into subcritical Stein manifolds, Israel J. Math. 127 (2002), 221–244.Google Scholar
[BCo09] Biran, P., Cornea, O., Rigidity and uniruling for Lagrangian submanifolds, Geom. Topol. 13 (2009), 2881–2989.Google Scholar
[Bo54] Bott, R., Nondegenerate critical manifolds, Ann. Math. 60 (1954), 248–261.Google Scholar
[Bu10] Buhovsky, L., The Maslov class of Lagrangian tori and quantum products in Floer cohomology, J. Topol. Anal. 2 (2010), 57–75.Google Scholar
[BO13] Buhovsky, L., Ostrover, A., On the uniqueness of Hofer's geometry, Geom. Funct. Anal. 21 (2011), no. 6, 1296–1330.Google Scholar
[BS10] Buhovsky, L., Seyfaddini, S., Uniqueness of generating Hamiltonians for continuous Hamiltonian flows, J. Symplectic Geom. 11 (2013), no. 1, 37–52.Google Scholar
[C09] Calegari, D., scl (Stable Commutator Length), MSJ Memoirs, vol. 20, Mathematical Society of Japan, 2009.
[Ch84] Chaperon, M., Une idée du type “géodésiques brisées” pour les systèmes of hamiltoniens, C. R. Acad. Sci. Paris Série I Math. 298 (1984), no. 13, 293–296.Google Scholar
[Che94] Chekanov, Yu. V., Hofer's symplectic energy and Lagrangian intersections, Contact and Symplectic Geometry (Cambridge, 1994), 296–306, Publications of the Newton Institute, 8, Cambridge University Press, Cambridge, 1996.
[Che96a] Chekanov, Yu. V., Critical points of quasifunctions, and generating families of Legendrian manifolds (in Russian), Funktsional. Anal. i Prilozhen. 30 (1996), no. 2, 56–69, 96; translation in Funct. Anal. Appl. 30 (1996), no. 2, 118–128.Google Scholar
[Che96b] Chekanov, Yu. V., Lagrangian tori in a symplectic vector space and global symplectomorphisms, Math. Z. 223 (1996), 547–559.Google Scholar
[Che98] Chekanov, Yu. V., Lagrangian intersections, symplectic energy, and areas of holomorphic curves, Duke Math. J. 95 (1998), 213–226.Google Scholar
[Che00] Chekanov, Yu. V., Invariant Finsler metrics on the space of Lagrangian embeddings, Math. Z. 234 (2000), 605–619.Google Scholar
[CS10] Chekanov, Yu. V., Schlenk, F., Notes on monotone Lagrangian twist tori, Electron. Res. Announc. Math. Sci. 17 (2010), 104–121.Google Scholar
[Chen73] Chen, K. T., Iterated integrals of differential forms and loop space homology, Ann. Math. 97 (1973), 217–246.Google Scholar
[Cher55] Chern, S. S., An elementary proof of the existence of isothermal parameters on a surface, Proc. Amer. Math. Soc. 6 (1955), 771–782.Google Scholar
[Cher67] Chern, S. S., Complex Manifolds without Potential Theory, Van NostrandMathematical Studies, No. 15 D. Van Nostrand Co., Inc., Princeton, NJ, 1967.
[Cho08] Cho, C.-H., Counting real J-holomorphic discs and spheres in dimension four and six, J. Korean Math. Soc. 45 (2008), no. 5, 1427–1442.Google Scholar
[CO06] Cho, C.-H., Oh, Y.-G., Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds, Asian J. Math. 10 (2006), 773–814.Google Scholar
[Co78] Conley, C., Isolated Invariant Sets and theMorse Index, CBMS Regional Conference Series in Mathematics, 38. American Mathematical Society, Providence, RI, 1978.
[CZ83] Conley, C., Zehnder, E., The Birkhoff–Lewis fixed point theorem and a conjecture of V. I. Arnold, Invent. Math. 73 (1983), 33–49.Google Scholar
[CZ84] Conley, C., Zehnder, E., Morse-type index theory for flows and periodic solutions of Hamiltonian equations, Commun. Pure Appl. Math. 37 (1984), 207–253.Google Scholar
[Cr99] Crainic, M., Cyclic cohomology of étale groupoids: the general case, K-Theory 17 (1999), 319–362.Google Scholar
[D09] Damian, M., Constraints on exact Lagrangians in cotangent bundles of manifolds fibered over the circle, Comment. Math. Helv. 84 (2009), 705–746.Google Scholar
[DM69] Deligne, P., Mumford, D., The irreducibility of the space of curves of given genus, IHES Publ. Math. 36 (1969), 75–109.Google Scholar
[Di58] Dirac, P., The Principles of Quantum Mechanics, 4th edn., Oxford University Press, Oxford, 1958.
[Do86] Donaldson, S. K., Connections, cohomology and the intersection forms of 4-manifolds, J. Diff. Geom. 24 (1986), 275–341.Google Scholar
[EL51] Ehresmann, C., Libermann, P., Sur les structures presque hermitiennes isotropes, C. R. Acad. Sci. Paris 232 (1951), 1281–1283.Google Scholar
[EkH89] Ekeland, I., Hofer, H., Symplectic topology and Hamiltonian dynamics, Math. Z. 200 (1989), 355–378.Google Scholar
[EkH90] Ekeland, I., Hofer, H., Symplectic topology and Hamiltonian dynamics II, Math. Z. 203 (1990), 553–567.Google Scholar
[El87] Eliashberg, Y., A theorem on the structure of wave fronts and its application in symplectic topology (in Russian), Funktsional. Anal. i Prilozhen. 21 (1987), no. 3, 65–72, 96.Google Scholar
[EG91] Eliashberg, Y., Gromov, M., Convex symplectic manifolds, in Several Complex Variables and Complex Geometry (Santa Cruz, CA 1989), Proc. Sympos. Pure Math. 52 Part 2. Amer. Math. Soc., Providence, RI (1991), 135–162.
[EP97] Eliashberg, Y., Polterovich, L., The problem of Lagrangian knots in fourmanifolds, Geometric Topology (Athens, GA, 1993), 313–327, AMS/IP Stud. Adv. Math., 2.1. American Mathematical Society, Providence, RI, 1997.
[EP10] Eliashberg, Y., Polterovich, L., Symplectic quasi-states on the quadric surface and Lagrangian submanifolds, arXiv:1006.2501.
[En00] Entov, M., K-area, Hofer metric and geometry of conjugacy classes in Lie groups, Invent. Math. 146 (2000), 93–141.Google Scholar
[En04] Entov, M., Commutator length of symplectomorphisms, Comment.Math. Helv. 79 (2004), 58–104.Google Scholar
[EnP03] Entov, M., Polterovich, L., Calabi quasimorphism and quantum homology, Internat. Math. Res. Notices no. 30 (2003), 1635–1676.Google Scholar
[EnP06] Entov, M., Polterovich, L., Quasi-states and symplectic intersections, Comment. Math. Helv. 81 (2006), 75–99.Google Scholar
[EnP09] Entov, M., Polterovich, L., Rigid subsets of symplectic manifolds, Compositio Math. 145 (2009), 773–826.Google Scholar
[Ev98] Evans, L., Partial Differential Equations. American Mathematical Society, Providence, RI, 1998.
[Fa05] Fathi, A., Weak KAM Theorem in Lagrangian Dynamics, book manuscript, 7th preliminary version, 2005 (available online).
[Fe69] Federer, H., Geometric Measure Theory, Die Grundlehren der mathematischen Wissenschaften 153. Berlin: Springer, 1969.
[Fl87] Floer, A., Morse theory for fixed points of symplectic diffeomorphisms, Bull. Amer. Math. Soc. (N.S.) 16 (1987), no. 2, 279–281.Google Scholar
[Fl88a] Floer, A., The unregularized gradient flow of the symplectic action, Commun. Pure Appl. Math. 43 (1988), 576–611.Google Scholar
[Fl88b] Floer, A., Morse theory for Lagrangian intersections, J. Diff. Geom. 28 (1988), 513–547.Google Scholar
[Fl88c] Floer, A., An instanton-invariant for 3-manifolds, Commun. Math. Phys. 118 (1988), no. 2, 215–240.Google Scholar
[Fl89a] Floer, A., Witten's complex and infinite-dimensional Morse theory, J. Diff. Geom. 30 (1989), 207–221.Google Scholar
[Fl89b] Floer, A., Symplectic fixed points and holomorphic spheres, Commun. Math. Phys. 120 (1989), 575–611.Google Scholar
[FH93] Floer, A., Hofer, H., Coherent orientations for periodic orbit problems in symplectic geometry, Math. Z. 212 (1993), 13–38.Google Scholar
[FHS95] Floer, A., Hofer, H., Salamon, D., Transversality in elliptic Morse theory for the symplectic action, Duke Math. J. 80 (1995), 251–292.Google Scholar
[Fol99] Folland, G., Real Analysis, 2nd edn., Wiley Interscience, New York, 1999.
[FU84] Freed, D., Uhlenbeck, K., Instantons and Four-Manifolds, Mathematical Sciences Research Institute Publications, 1. Springer, New York, 1984.
[Fu93] Fukaya, K., Morse homotopy, A∞-category, and Floer homologies, Proceedings of GARC Workshop on Geometry and Topology ’93 (Seoul, 1993), 1–102, Lecture Notes Series, 18. Seoul National University, Seoul, 1993.
[Fu06] Fukaya, K., Application of Floer homology of Langrangian submanifolds to symplectic topology, in Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology, 231–276, NATO Sci. Ser. II Math. Phys. Chem., 217. Springer, Dordrecht, 2006.
[FOh97] Fukaya, K., Oh, Y.-G., Zero-loop open strings in the cotangent bundle and Morse homotopy, Asian J. Math. 1 (1997), 96–180.Google Scholar
[FOOO07] Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K., Lagrangian surgery and metamorphosis of pseudo-holomorphic polygons, preprint, 2007; available at http://www.math.wisc.edu/oh/Chapter10071117.pdf.
[FOOO09] Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K., Lagrangian Intersection Floer Theory: Anomaly and Obstruction, AMS/IP Studies in Advanced Mathematics, vol. 46. American Mathematical Society/International Press, 2009.
[FOOO10a] Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K., Anchored Lagrangian submanifolds and their Floer theory, Mirror Symmetry and Tropical Geometry, 15–54, Contemporary Mathematical, vol. 527. American Mathematical Society, Providence, RI, 2010.
[FOOO10b] Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K., Lagrangian Floer theory on compact toric manifolds I, Duke Math. J. 151 (2010), 23–174.Google Scholar
[FOOO11a] Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K., Lagrangian Floer theory on compact toric manifolds II; Bulk deformations, Selecta Math. (N.S.) 17 (2011), no. 3, 609–711.Google Scholar
[FOOO11b] Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K., Spectral invariants with bulk, quasimorphisms and Lagrangian Floer theory, preprint 2011, arXiv:1105.5123.
[FOOO12a] Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K., Toric degeneration and nondisplaceable Lagrangian tori in S 2 × S 2, Internat. Math. Res. Notices, No. 13 (2012), 2942–2993.Google Scholar
[FOOO12b] Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K., Technical details on Kuranishi structure and virtual fundamental chain, preprint 2012, arXiv: 1209.4410.
[FOOO13] Fukaya, K., Oh, Y.-G., Ohta, H., Ono, K., Displacement of polydisks and Lagrangian Floer theory, J. Symplectic Geom. 11 (2013), 1–38.Google Scholar
[FOn99] Fukaya, K., Ono, K., Arnold conjecture and Gromov–Witten invariants, Topology 38 (1999), 933–1048.Google Scholar
[FSS08] Fukaya, K., Seidel, P., Smith, I., Exact Lagrangian submanifolds in simply-connected cotangent bundles, Invent. Math. 172 (2008), 1–27.Google Scholar
[GG97] Gambaudo, J.-M., Ghys, É., Enlacements asymptotiques, Topology 36 (1997), 1355–1379.Google Scholar
[GG04] Gambaudo, J.-M., Ghys, É., Commutators and diffeomorphisms of surfaces, Ergod. Theory Dynam. Syst. 24 (2004), 1591–1617.Google Scholar
[Ga97] Gauduchon, P., Hermitian connection and Dirac operators, Boll. Unione Mat. Ital. B (7) 11 (1997), suppl. 2, 257–288.Google Scholar
[GS68] Gelfand, I.M., Shilov, G.E., Generalized Functions, vol. 2. Academic Press, New York, 1968.
[Geo13] Georgieva, P., The orientability problem in open Gromov–Witten theory, Geom. Topol. 17 (2013), no. 4, 2485–2512.Google Scholar
[GJP91] Getzler, E., Jones, D. S., Petrack, S., Differential forms on loop spaces and the cyclic bar complex, Topology 30 (1991), 339–371.Google Scholar
[GT77] Gilbarg, D., Trudinger, N., Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften, vol. 224. Springer, Berlin, 1977.
[Go80] Goldstein, H., Classical Mechanics, 2nd edn., Addison-Wesley Series in Physics. Addison-Wesley Publishing Co., Reading, MA, 1980.
[Gh06] Ghys, É., Knots and dynamics, Proceedings of ICM-2006 vol. 1, 247–277, Madrid, EMS, 2006.
[Gom95] Gompf, R., A new construction for symplectic 4-manifolds, Ann. Math. 142 (1995), 527–595.Google Scholar
[Gom98] Gompf, R.Symplectically aspherical manifolds with nontrivial π2, Math. Res. Lett. 5 (1998), 599–603.Google Scholar
[GLSW83] Gotay, M., Lashof, R., Śniatycki, J., Weinstein, A., Closed forms on symplectic fibre bundles, Comment. Math. Helv. 58 (1983), no. 4, 617–621.Google Scholar
[Gr85] Gromov, M., Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307–347.Google Scholar
[Gr88] Gromov, M., Metric Structures for Riemannian and Non-Riemannian spaces, Progress inMathematics, vol. 152. Birkäuser, Boston, MA, 1998.
[Gr96] Gromov, M., Positive curvature, macroscopic dimension, spectral gaps and higher signatures, Functional Analysis on the Eve of the 21st Century, Vol. II (New Brunswick, NJ, 1993), 1–213, Progress in Mathematics, vol. 132. Birkhäuser, Boston, MA, 1996.
[GrSi03] Gross, M., Siebert, B., Affine manifolds, log structures, and mirror symmetry, Turkish J. Math. 27 (2003), 33–60.Google Scholar
[GLS96] Guillemin, V., Lerman, E., Sternberg, S., Symplectic Fibrations and Multiplicity Diagrams. Cambridge University Press, Cambridge, 1996.
[GS77] Guillemin, V., Sternberg, S., Geometric Asymptotics, Mathematical Surveys, No. 14. American Mathematical Society, Providence, RI, 1977.
[He78] Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces, Pure and AppliedMathematics, vol. 80. Academic Press, Inc., New York, 1978.
[HM04] Henriques, A.,Metzler, S., Presentations of noneffective orbifolds, Trans. Amer. Math. Soc. 356 (2004), 2481–2499.Google Scholar
[Hi99] Hitchin, N., Lectures on special Lagrangian submanifolds, Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999), 151–182, AMS/IP Stud. Adv. Math., 23. American Mathematical Society, Providence, RI, 2001.
[H85] Hofer, H., Lagrangian embeddings and critical point theory. Ann. Inst. H. Poincaré, Anal. Non Linéaire, 2 (1985), 407–462.Google Scholar
[H90] Hofer, H., On the topological properties of symplectic maps, Proc. Royal Soc. Edinburgh 115 (1990), 25–38.Google Scholar
[H93] Hofer, H., Estimates for the energy of a symplectic map, Comment.Math. Helv. 68 (1993), 48–72.Google Scholar
[H08] Hofer, H., Polyfolds and a general Fredholm theory, preprint, arXiv:0809.3753.
[HS95] Hofer, H., Salamon, D., Floer homology and Novikov rings, in The Floer Memorial Volume, Progress in Mathematics, 133. Birkhaüser, Basel, 1995, pp. 483–524.
[HWZ02] Hofer, H.,Wysocki, K., Zehnder, E., Finite energy cylinder of small area, Ergod. Theory Dynam. Syst. 22 (2002), 1451–1486.Google Scholar
[HWZ07] Hofer, H., Wysocki, K., Zehnder, E., A general Fredholm theory, I: A splicing-based differential geometry, J. Eur.Math. Soc. (JEMS) 9 (2007), 841–876.Google Scholar
[HZ94] Hofer, H., Zehnder, E., Symplectic Invariants and Hamiltonian Dynamics. Birkhäuser, Basel, 1994.
[Hor71] Hörmander, L., Fourier integral operators. I, Acta Math. 127 (1971), 79–183.Google Scholar
[KL01] Katz, S., Liu, C. M., Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc, Adv. Theor. Math. Phys. 5 (2001), no. 1, 1–49.Google Scholar
[KL03] Kerman, E., Lalonde, F., Length minimizing Hamiltonian paths for symplectically aspherical manifolds, Ann. Inst. Fourier, 53 (2003), 1503–1526.Google Scholar
[Ko03] Kobayashi, S., Natural connections in almost complex manifolds, Explorations in Complex and Riemannian Geometry, 153–169, Contemporary Mathematics, 332. American Mathematical Society, Providence, RI, 2003.
[KN96] Kobayashi, S., Nomizu, K., Foundations of Differential Geometry, vol. 2, John Wiley & Sons, New York, 1996, Wiley Classics Library Edition.
[Kon95] Kontsevich, M., Enumeration of rational curves via torus actions, in The Moduli Space of Curves, Progress in Mathematics 129, pp. 335–368. Birkhäuser, Basel, 1995.
[Kon03] Kontsevich, M., Deformation quantization of Poisson manifolds. Lett. Math. Phys. 66 (2003), 157–216.Google Scholar
[Kor16] Korn, A., Zwei Anwendungen der Methode der sukzessiven Annäherungen. Schwarz Abhandlungen (1916), 215–219.Google Scholar
[KM07] Kronheimer, P., Mrowka, T., Monopoles and Three-Manifolds. New Mathematical Monographs, 10. Cambridge University Press, Cambridge, 2007.
[KO00] Kwon, D., Oh, Y.-G., Structure of the image of (pseudo)-holomorphic discs with totally real boundary condition, Appendix 1 by Jean-Pierre Rosay. Commun. Anal. Geom. 8 (2000), no. 1, 31–82.Google Scholar
[L04] Lalonde, F., A field theory for symplectic fibrations over surfaces, Geom. Top. 8 (2004), 1189–1226.Google Scholar
[LM95a] Lalonde, F., McDuff, D., The geometry of symplectic energy, Ann. Math. 141 (1995), 349–371.Google Scholar
[LM95b] Lalonde, F., McDuff, D., Hofer's L∞-geometry: energy and stability of Hamiltonian flows I, II, Invent. Math. (1995), 1–33, 35–69.Google Scholar
[LMP98] Lalonde, F., McDuff, D., Polterovich, L., On the flux conjectures, Geometry, Topology, and Dynamics (Montreal, PQ, 1995), 69–85, CRM Proc. Lecture Notes, 15. American Mathematical Society, Providence, RI, 1998.
[La83] Lang, S., Real Analysis, 2nd edn. Addison-Wesley Publishing Company, Reading, MA, 1983.
[La02] Lang, S., Introduction to Differentiable Manifolds, 2nd edn., Universitext. Springer, New York, 2002.
[Lat91] Latour, F., Transversales lagrangiennes, périodicité de Bott et formes généatrices pour une immersion lagrangienne dans un cotangent, Ann. Sci. École Norm. Sup. (4) 24 (1991), no. 1, 3–55.Google Scholar
[LS85] Laudenbach, F., Sikorav, J.-C., Persistence of intersection with the zero section during a Hamiltonian isotopy into a cotangent bundle, Invent. Math. 82 (1985), no. 2, 349–357Google Scholar
[Law80] Lawson, H. B., Lectures on Minimal Submanifolds. Publish or Perish, Berkeley, CA, 1980.
[Laz00] Lazzarini, L., Existence of a somewhere injective pseudo-holomorphic disc, Geom. Funct. Anal. 10 (2000), no. 4, 829–862.Google Scholar
[LO96] Le, H. V., Ono, K., Perturbation of pseudo-holomorphic curves, Addendum to: “Notes on symplectic 4-manifolds with b+2 = 1, II”, Internat. J. Math. 7 (1996), no. 6, 755–770 by H. Ohta and Ono, Internat. J. Math. 7 (1996), no. 6, 771–774.Google Scholar
[LiT98] Li, J., Tian, G., Virtual moduli cycles and Gromov–Witten invariants of algebraic varieties, J. Amer. Math. Soc. 11 (1998), no. 1, 119–174.Google Scholar
[Li16] Lichtenstein, L., Zur Theorie der konformen Abbildung, Bull. Internat. Acad. Sci. Cracovie. Cl. Sci. Math. Nat. Série A. (1916), 192–217.Google Scholar
[LT98] Liu, G., Tian, G., Floer homology and Arnold conjecture, J. Diff. Geom. 49 (1998), 1–74.Google Scholar
[LT99] Liu, G., Tian, G., On the equivalence of multiplicative structures in Floer homology and quantum homology, Acta Math. Sinica 15 (1999), 53–80.Google Scholar
[L02] Liu, M. C., Moduli of J-holomorphic curves with Lagrangian boundary coniditions and open Gromov–Witten invariants for an S 1-equivariant pair, preprint, 2002, arXiv:math/0210257.
[LM85] Lockhard, R., McOwen, R., Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 12 (1985), no. 3, 409–447.Google Scholar
[LuG96] Lu, Guangcun, The Weinstein conjecture on some symplectic manifolds containing holomorphic spheres, Kyushu J. Math. 50 (1996), 331–351.Google Scholar
[MW74] Marsden, J., Weinstein, A., Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5 (1974), 121–130.Google Scholar
[McC85] McCleary, J., User's Guide to Spectral Sequences, Mathematics Lecture Series 12. Publish or Perish, Wilmington, DE, 1985.
[Mc87] McDuff, D., Examples of symplectic structures, Invent. Math. 89 (1987), 13–36.Google Scholar
[Mc90] McDuff, D., The structure of rational and ruled symplectic 4-manifolds, J. Amer. Math. Soc. 3 (1990), no. 3, 679–712.Google Scholar
[MSa94] McDuff, D., Salamon, D., Introduction to Symplectic Topology. Oxford University Press, Oxford, 1994.
[MSa04] McDuff, D., Salamon, D., J-holomorphic Curves and Symplectic Topology. AMS, Providence, RI, 2004.
[MSl01] McDuff, D., Slimowitz, J., Hofer–Zehnder capacity and length minimizing Hamiltonian paths, Geom. Topol. 5 (2001), 799–830.Google Scholar
[Mi99] Milinković, D., Morse homology for generating functions of Lagrangian submanifolds, Trans. Amer. Math. Soc. 351 (1999), 3953–3974.Google Scholar
[Mi00] Milinković, D., On equivalence of two constructions of invariants of Lagrangian submanifolds, Pacific J. Math. 195 (2000), no. 2, 371–415.Google Scholar
[MiO95] Milinković, D., Oh, Y.-G., Generating functions versus action functional: Stable Morse theory versus Floer theory, Geometry, Topology, and Dynamics (Montreal, PQ, 1995), 107–125, CRM Proc. Lecture Notes, 15.
[MiO97] Milinković, D., Oh, Y.-G., Floer homology as the stable Morse homology, J. Korean Math. Soc. 34 (1997), 1065–1087.Google Scholar
[Mil65] Milnor, J., Lectures on the H-cobordism Theorem, Notes by L., Siebenmann and J., Sondow. Princeton University Press, Princeton, NJ, 1965.
[MSt74] Milnor, J., Stasheff, J., Characteristic Classes, Ann. Math. Studies. Princeton University Press, Princeton, NJ, 1974.
[MVZ12] Monzner, A., Vichery, N, Zapolsky, F., Partial quasimorphisms and take to next line quasistates on cotangent bundles, and symplectic homogenization, J. Mod. Dyn. 6 (2012), no. 2, 205–249.Google Scholar
[Mo66] Morrey, C. B., Multiple Integrals in the Calculus of Variations. Springer, New York, 1966.
[Mo65] Moser, J., Volume elements on manifolds, Trans. Amer. Math. Soc. 120 (1965), 286–294.Google Scholar
[MFK94] Mumford, D., Fogarty, J., Kirwan, F., Geometric Invariant Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (2), 34, 3rd edn. Springer, Berlin, 1994.
[Mue08] Müller, S., The group of Hamiltonian homeomorphisms in the L∞-norm, J. Korean Math. Soc. 45 (2008), No. 6, 1769–1784.Google Scholar
[MT09] Mundet i Riera, I., Tian, G., A compactification of the moduli space of twisted holomorphic maps, Adv. Math. 222 (2009), 1117–1196.Google Scholar
[Na09] Nadler, D., Microlocal branes are constructible sheaves, Selecta Math. (N.S.) 15 (2009), 563–619.Google Scholar
[NaZ09] Nadler, D., Zaslow, E., Constructible sheaves and the Fukaya category, J. Amer. Math. Soc. 22 (2009), 233–286.Google Scholar
[Nas56] Nash, J., The imbedding problem for Riemannian manifolds, Ann. Math. (2) 63 (1956), 20–63.Google Scholar
[NiW63] Nijenhuis, A., Wolf, W., Some integration problems in almost-complex and complex manifolds, Ann. Math. 77 (1963), 424–489.Google Scholar
[No81] Novikov, S. P., Multivalued functions and functionals. An analogue of the Morse theory (in Russian), Dokl. Akad. Nauk SSSR 260 (1981), no. 1, 31–35.Google Scholar
[No82] Novikov, S. P., The Hamiltonian formalism and a multivalued analogue of Morse theory (in Russian), Uspekhi Mat. Nauk 37 (1982), no. 5(227), 3–49, 248.Google Scholar
[Oh92] Oh, Y.-G., Removal of boundary singularities of pseudo-holomorphic curves with Lagrangian boundary conditions, Commun. Pure Appl. Math. 45 (1992), 121–139.Google Scholar
[Oh93a] Oh, Y.-G., Floer cohomology of Lagrangian intersections and pseudoholomorphic disks. I, Commun. Pure Appl. Math. 46 (1993), 949–993.Google Scholar
[Oh93b] Oh, Y.-G., Floer cohomology of Lagrangian intersections and pseudoholomorphic disks. II; (ℂPn,ℝPn), Commun. Pure Appl. Math. 46 (1993), 995–1012.Google Scholar
[Oh95a] Oh, Y.-G., Addendum to: “Floer cohomology of Lagrangian intersections and pseudo-holomorphic disks. I”, Commun. Pure Appl. Math. 48 (1995), no. 11, 1299–1302,Google Scholar
[Oh95b] Oh, Y.-G., Riemann–Hilbert problem and application to the perturbation theory of analytic discs, Kyungpook Math. J. 35 (1995), 39–75.Google Scholar
[Oh96a] Oh, Y.-G., Fredholm theory of holomorphic discs under the perturbation of boundary conditions, Math. Z. 222 (1996), 505–520.Google Scholar
[Oh96b] Oh, Y.-G., Floer cohomology, spectral sequences, and the Maslov class of Lagrangian embeddings, Internat. Math. Res. Notices no. 7 (1996), 305–346.Google Scholar
[Oh96c] Oh, Y.-G., Relative Floer and quantum cohomology and the symplectic topology of Lagrangian submanifolds, in Contact and Symplectic Geometry (Cambridge, 1994), 201–267, Publications of the Newton Institute, 8. Cambridge University Press, Cambridge, 1996.
[Oh97a] Oh, Y.-G., On the structure of pseduo-holomorphic discs with totally real boundary conditions, J. Geom. Anal. 7 (1997), 305–327.Google Scholar
[Oh97b] Oh, Y.-G., Symplectic topology as the geometry of action functional, I, J. Diff. Geom. 46 (1997), 499–577.Google Scholar
[Oh97c] Oh, Y.-G., Gromov–Floer theory and disjunction energy of compact Lagrangian embeddings, Math. Res. Lett. 4 (1997), 895–905.Google Scholar
[Oh99] Oh, Y.-G., Symplectic topology as the geometry of action functional, II, Commun. Anal. Geom. 7 (1999), 1–55.Google Scholar
[Oh02] Oh, Y.-G., Chain level Floer theory and Hofer's geometry of the Hamiltonian diffeomorphism group, Asian J. Math. 6 (2002), 579–624; Erratum 7 (2003), 447–448.Google Scholar
[Oh05a] Oh, Y.-G., Normalization of the Hamiltonian and the action spectrum, J. Korean Math. Soc. 42 (2005), 65–83.Google Scholar
[Oh05b] Oh, Y.-G., Spectral invariants and length minimizing property of Hamiltonian paths, Asian J. Math. 9 (2005), 1–18.Google Scholar
[Oh05c] Oh, Y.-G., Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds, in The Breadth of Symplectic and Poisson Geometry: Festschrift in Honor of Alan Weinstein, Progress in Mathematics 232, 525–570. Birkhäuser, Boston, MA, 2005.
[Oh05d] Oh, Y.-G., Spectral invariants, analysis of the Floer moduli space and geometry of Hamiltonian diffeomorphisms, Duke Math. J. 130 (2005), 199–295.Google Scholar
[Oh06a] Oh, Y.-G., Lectures on Floer theory and spectral invariants of Hamiltonian flows, in Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology, 321–416, NATO Sci. Ser. II Math. Phys. Chem., 217. Springer, Dordrecht, 2006.
[Oh06b] Oh, Y.-G., C0-coerciveness of Moser's problem and smoothing area preserving homeomorphisms, preprint; arXiv:math/0601183.
[Oh07] Oh, Y.-G., Locality of continuous Hamiltonian flows and Lagrangian intersections with the conormal of open subsets, J. Gökova Geom. Top. 1 (2007), 1–32.Google Scholar
[Oh09a] Oh, Y.-G., Floer mini-max theory, the Cerf diagram, and the spectral invariants, J. Korean Math. Soc. 46 (2009), 363–447.Google Scholar
[Oh09b] Oh, Y.-G., Unwrapped continuation invariance in Lagrangian Floer theory: energy and C0 estimates, preprint 2009, arXiv:0910.1131.
[Oh10] Oh, Y.-G., The group of Hamiltonian homeomorphisms and continuous Hamiltonian flows, in Symplectic Topology and Measure Preserving Dynamical Systems, 149–177, Contemporary Mathematics, 512. American Mathematical Society, Providence, RI, 2010.
[Oh11a] Oh, Y.-G., Higher jet evaluation transversality of J-holomorphic curves, J. Korean Math. Soc. 48 (2011), no. 2, 341–365.Google Scholar
[Oh11b] Oh, Y.-G., Localization of Floer homology of engulfable topological Hamiltonian loops, Commun. Info. Syst. 13 (2013), no. 4, 399–443 in a special volume in honor of Marshall Slemrod's 70th birthday.Google Scholar
[OhM07] Oh, Y.-G., Müller, S., The group of Hamiltonian homeomorphisms and C0-symplectic topology, J. Symplectic Geom. 5 (2007), 167–219.Google Scholar
[OhP05] Oh, Y.-G., Park, J. S., Deformations of coisotropic submanifolds and strong homotopy Lie algebroids, Invent. Math. 161 (2005), 287–360.Google Scholar
[OhW12] Oh, Y.-G., Wang, R., Canonical connection and contact Cauchy–Riemann maps on contact manifolds I. preprint 2012, arXiv:1215.5186.
[OhZ09] Oh, Y.-G., Zhu, K., Embedding property of J-holomorphic curves in Calabi–Yau manifolds for generic J, Asian J. Math. 13 (2009), 323–340.Google Scholar
[OhZ11a] Oh, Y.-G., Zhu, K., Thick–thin decomposition of Floer trajectories and adiabatic gluing, preprint, 2011, arXiv:1103.3525.
[OhZ11b] Oh, Y.-G., Zhu, K., Floer trajectories with immersed nodes and scaledependent gluing, J. Symplectic Geom. 9 (2011), 483–636.Google Scholar
[On95] Ono, K., On the Arnold conjecture for weakly monotone symplectic manifolds, Invent. Math. 119 (1995), no. 3, 519–537.Google Scholar
[On06] Ono, K., Floer–Novikov cohomology and the flux conjecture, Geom. Funct. Anal. 16 (2006), 981–1020.Google Scholar
[Os03] Ostrover, Y., A comparison of Hofer's metrics on Hamiltonian diffeomorphisms and Lagrangian submanifolds, Commun. Contemp. Math. 5 (2003), 803–812.Google Scholar
[OW05] Ostrover, Y., Wagner, R., On the extremality of Hofer's metric on the group of Hamiltonian diffeomorphisms, Internat. Math. Res. Notices (2005), no. 35, 2123–2141.Google Scholar
[Pa94] Pansu, P., Compactness. Holomorphic curves in symplectic geometry, 233–249, Progress in Mathematics, 117. Birkhäuser, Basel, 1994.
[PW93] Parker, T., Wolfson, J., Pseudoholomorphic maps and bubble trees, J. Geom. Anal. 3 (1993), 63–98.Google Scholar
[Pe59] Peetre, J., Une caractérisation abstraite des opérateurs différentiels, Math. Scand. 7 (1959), 211–218; Rectifications, ibid. 8 (1960), 116–120.Google Scholar
[Pi94] Piunikhin, S., Quantum and Floer cohomology have the same ring structure, preprint 1994, arXiv:hep-th/9401130.
[PSS96] Piunikhin, S., Salamon, D., Schwarz, M., Symplectic Floer–Donaldson theory and quantum cohomology, Publications of the Newton Institute 8, ed. by Thomas, C. B., 171–200. Cambridge University Press, Cambridge, 1996.
[Po91a] Polterovich, L., The Maslov class of the Lagrange surfaces and Gromov's pseudo-holomorphic curves, Trans. Amer. Math. Soc. 325 (1991), 217–222.Google Scholar
[Po91b] Polterovich, L., The surgery of Lagrange submanifolds, Geom. Funct. Anal. 1 (1991), 198–210.Google Scholar
[Po93] Polterovich, L., Symplectic displacement energy for Lagrangian submanifolds, Ergod. Theory Dynam. Syst., 13 (1993), 357–367.Google Scholar
[Po96] Polterovich, L., Gromov's K-area and symplectic rigidity, Geom. Funct. Anal. 6 (1996), no. 4, 726–739.Google Scholar
[Po98a] Polterovich, L., Geometry on the group of Hamiltonian diffeomorphisms, Doc. Math. J. DMV, Extra Volume ICM 1998, Vol. II, pp 401–410.
[Po98b] Polterovich, L., Hofer's diameter and Lagrangian intersections, Internat. Math. Res. Notices, 1998 No. 4, 217–223.Google Scholar
[Po01] Polterovich, L., The Geometry of the Group of Symplectic Diffeomorphisms, Lectures in Mathematics ETH Zürich. Birkhäuser, Basel, 2001.
[Poz99] Poźniak, M., Floer homology, Novikov rings and clean intersections, Northern California Symplectic Geometry Seminar, 119–181, Amer. Math. Soc. Transl. Ser. 2, 196. American Mathematical Society, Providence, RI, 1999.
[Ra78] Rabinowitz, P., Periodic solutions of Hamiltonian systems, Commun. Pure Appl. Math. 31 (1978), 157–184.Google Scholar
[RS93] Robbin, J., Salamon, D., The Maslov index for paths, Topology 32 (1993), 827–844.Google Scholar
[RS95] Robbin, J., Salamon, D., The spectral flow and the Maslov index, Bull. London Math. Soc. 27 (1995), 1–33.Google Scholar
[RS01] Robbin, J., Salamon, D., Asymptotic behaviour of holomorphic strips, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001), 573–612.Google Scholar
[RS06] Robbin, J., Salamon, D. A construction of the Deligne–Mumford orbifold, J. Eur. Math. Soc. (JEMS) 8 (2006), no. 4, 611–699; Corrigendum, ibid. 9 (2007), no. 4, 901–205.Google Scholar
[Ru96] Ruan, Y., Topological sigma model and Donaldson-type invariants in Gromov theory, Duke Math. J. 83 (1996), 461–500.Google Scholar
[Ru99] Ruan, Y., Virtual neighborhoods and pseudo-holomorphic curves, Proceedings of 6th Gökova Geometry–Topology Conference. Turkish J. Math. 23 (1999), 161–231.Google Scholar
[RT95a] Ruan, Y., Tian, G., A mathematical theory of quantum cohomology, J. Diff. Geom. 42 (1995), 259–367.Google Scholar
[RT95b] Ruan, Y., Tian, G., Bott-type symplectic Floer cohomology and its multiplication structures, Math. Res. Lett. 2 (1995), 203–219.Google Scholar
[Rud73] Rudin, W., Functional Analysis. McGraw-Hill Book Co., New York, 1973.
[SU81] Sacks, J., Uhlenbeck, K., The existence of minimal immersions of 2 spheres, Ann. Math. 113 (1981), 1–24.Google Scholar
[SZ92] Salamon, D., Zehnder, E., Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Commun. Pure Appl. Math. 45 (1992), 1303–1360.Google Scholar
[Sc84] Schoen, R., Analytic aspects of the harmonic map problem, in Lectures on Partial Differential Equations, S. S., Chern, ed. Springer, Berlin, 1984.
[ScU83] Schoen, R., Uhlenbeck, K., Boundary regularity and the Dirichlet problem for harmonic maps, J. Diff. Geom. 18 (1983), 253–268.Google Scholar
[Sch06] Schlenk, F., Applications of Hofer's geometry to Hamiltonian dynamics, Comment. Math. Helv. 81 (2006), no. 1, 105–121.Google Scholar
[Schw93] Schwarz, M., Morse Homology, Progress in Mathematics, 111. Birkhäuser, Basel, 1993.
[Schw95] Schwarz, M., Thesis, ETH Zürich, 1995.
[Schw00] Schwarz, M., On the action spectrum for closed symplectically aspherical manifolds, Pacific J. Math. 193 (2000), 419–461.Google Scholar
[SS88] Seeley, R., Singer, I. M., Extending ∂ to singular Riemann surfaces, J. Geom. Phys. 5 (1988), 121–136.Google Scholar
[Se97] Seidel, P., π1 of symplectic automorphism groups and invertibles in quantum homology rings, Geom. Funct. Anal. 7 (1997), 1046–1095.Google Scholar
[Se03a] Seidel, P., A long exact sequence for symplectic Floer homology, Topology 42 (2003), 1003–1064.Google Scholar
[Se03b] Seidel, P., Homological mirror symmetry for the quartic surface, preprint 2003, math.SG/0310414.
[Se06] Seidel, P., A biased view of symplectic cohomology, Current Developments in Mathematics, 2006, 211–253. International Press, Somerville, MA, 2008.
[Se08] Seidel, P., Fukaya Categories and Picard–Lefshetz Theory, Zürich Lectures in Advanced Mathematics. European Mathematical Society, Zurich, 2008.
[Sey13a] Seyfaddini, S., C0-limits of Hamiltonian paths and the Oh–Schwarz spectral invariants, Int. Math. Res. Notices, 2013, no. 21, 4920–4960.Google Scholar
[Sey13b] Seyfaddini, S., The displaced disks problem via symplectic topology, C. R. Math. Acad. Sci. Paris 351 (2013), no. 21–22, 841–843.Google Scholar
[Sie99] Siebert, B., Symplectic Gromov–Witten invariants, in New Trends in Algebraic Geometry, ed. Catanese, P., Reid, L. M. S. Lecture Notes 264. Cambridge University Press, Cambridge, 1999, 375–424.
[Sik87] Sikorav, J. C., Problèmes d'intersections et de points fixes en géométrie hamiltonienne, Comment. Math. Helv. 62 (1987), 62–73.Google Scholar
[Sik94] Sikorav, J. C., Some properties of holomorphic curves in almost complex manifolds, Chapter V of Holomorphic Curves in Symplectic Geometry, ed. Audin, M. and Lafontaine, J. Birkhäuser, Basel, 1994.
[Sik07] Sikorav, J. C., Approximation of a volume-preserving homeomorphism by a volume-preserving diffeomorphism, preprint, September 2007; available from http://www.umpa.ens-lyon.fr/symplexe.
[Sil98] de Silva, V., Products in the symplectic Floer homology of Lagrangian intersections, Ph D thesis, University of Oxford (1998).
[Sm61] Smale, S., Generalized Poincaré's conjecture in dimensions greater than four, Ann. Math. 74 (1961), 391–406.Google Scholar
[Sm65] Smale, S., An infinite dimensional version of Sard's theorem, Amer. J. Math. 87 (1965), 861–866.Google Scholar
[Spa08] Spaeth, P., Length minimizing paths in the Hamiltonian diffeomorphism group, J. Symplectic Geom. 6 (2008), no. 2, 159–187.Google Scholar
[Spi79] Spivak, M., A Comprehensive Introduction to Differential Geometry. Vols. I & II, 2nd edn. Publish or Perish, Wilmington, DE, 1979.
[SYZ01] Strominger, A., Yau, S.-T., Zaslow, E., Mirror symmetry is T-duality, Winter School on Mirror Symmetry, Vector Bundles and Lagrangian Submanifolds (Cambridge, MA, 1999), 333–347, AMS/IP Stud. Adv. Math., 23. American Mathematical Society, Providence, RI, 2001.
[Ta82] Taubes, C., Self-dual Yang–Mills connections on non-self-dual 4-manifolds, J. Diff. Geom. 17 (1982), 139–170.Google Scholar
[Th99] Theret, D., A complete proof of Viterbo's uniqueness theorem on generating functions, Topology Appl. 96 (1999), 249–266.Google Scholar
[Tr94] Traynor, L., Symplectic homology via generating functions, Geom. Funct. Anal. 4 (1994), 718–748.Google Scholar
[Ush08] Usher, M., Spectral numbers in Floer theories, Compositio Math. 144 (2008), 1581–1592.Google Scholar
[Ush10a] Usher, M., The sharp energy–capacity inequality, Commun. Contemp. Math. 12 (2010), no. 3, 457–473.Google Scholar
[Ush10b] Usher, M., Duality in filtered Floer–Novikov complexes, J. Topol. Anal. 2 (2010), 233–258.Google Scholar
[Ush11] Usher, M., Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds, Israel J. Math. 184 (2011), 1–57.Google Scholar
[Ush12] Usher, M., Many closed symplectic manifolds have infinite Hofer–Zehnder capacity, Trans. Amer. Math. Soc. 364 (2012), no. 11, 5913–5943.Google Scholar
[Ush13] Usher, M., Hofer's metrics and boundary depth, Ann. Sci. École Norm. Supér. (4) 46 (2013), no. 1, 57–128.Google Scholar
[Ust96] Ustilovsky, I., Conjugate points on geodesics of Hofer's metric, Diff. Geom. Appl. 6 (1996), 327–342.Google Scholar
[Va92] Vafa, C., Topological mirrors and quantum rings, in Essays on Mirror Manifolds, ed. S. T., Yau. International Press, Hong Kong, 1992.
[Via13] Vianna, R., On exotic Lagrangian tori in ℂP2, Geom. Top. 18 (2014), no. 4, 2419–2476.Google Scholar
[Via14] Vianna, R., Infinitely many exotic monotone Lagrangian tori in ℂP2, preprint 2014, arXiv:1409.2850.
[Vi88] Viterbo, C., Indice de Morse des points critiques obtenus par minimax, Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988), 221–225.Google Scholar
[Vi90] Viterbo, C., A new obstruction to embedding Lagrangian tori, Invent. Math. 100 (1990), 301–320.Google Scholar
[Vi92] Viterbo, C., Symplectic topology as the geometry of generating functions, Math. Ann. 292 (1992), 685–710.Google Scholar
[Vi99] Viterbo, C., Functors and computations in Floer homology with applications, I, Geom. Funct. Anal. 9 (1999), 985–1033.Google Scholar
[Vi06] Viterbo, C., Uniqueness of generating Hamiltonians for continuous Hamiltonian flows, Internat. Math. Res. Notices vol. 2006, Article ID 34028, 9 pages; Erratum, ibid., vol. 2006, Article ID 38784, 4 pages.Google Scholar
[Wb94] Weibel, C., An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics 38. Cambridge University Press, Cambridge, 1994.
[Wn73] Weinstein, A., Lagrangian submanifolds and Hamiltonian systems, Ann. Math. (2) 98 (1973), 377–410.Google Scholar
[Wn78] Weinstein, A., Bifurcations and Hamilton's principle, Math. Z. 159 (1978), 235–248.Google Scholar
[Wn83] Weinstein, A., The local structure of Poisson manifolds, J. Diff. Geom. 18 (1983), 523–557.Google Scholar
[Wn87] Weistein, A., Graduate courses given during 1987–1988 at the University of California-Berkeley.
[Wn90] Weinstein, A., Connections of Berry and Hannay type for moving Lagrangian submanifolds, Adv. Math. 82 (1990), 133–159.Google Scholar
[WW10] Wehrheim, K., Woodward, C., Functoriality for Lagrangian correspondences in Floer theory, Quantum Topol. 1 (2010), no. 2, 129–170.Google Scholar
[Wi91] Witten, W., Two dimensional gravity and intersection theory on moduli spaces, Surv. Differ. Geom. 1 (1991), 243–310.Google Scholar
[Wu12] Wu, W.-W., On an exotic Lagrangian torus in CP2, preprint 2012, arXiv:1201-2446.
[Ye94] Ye, R, Gromov's compactness theorem for pseudo holomorphic curves, Trans. Amer. Math. Soc. 342 (1994), 671–694.Google Scholar
[Yo69] Yorke, J., Periods of periodic solutions and the Lipschitz constant, Proc. Amer. Math. Soc. 22 (1969), 509–512.Google Scholar
[Z93] Zwiebach, B., Closed string field theory: Quantum action and the Batalin–Vilkovisky master equation, Nucl. Phys. B 390 (1993), 33–152.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • Yong-Geun Oh, Pohang University of Science and Technology, Republic of Korea
  • Book: Symplectic Topology and Floer Homology
  • Online publication: 05 September 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781316271889.017
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • Yong-Geun Oh, Pohang University of Science and Technology, Republic of Korea
  • Book: Symplectic Topology and Floer Homology
  • Online publication: 05 September 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781316271889.017
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • Yong-Geun Oh, Pohang University of Science and Technology, Republic of Korea
  • Book: Symplectic Topology and Floer Homology
  • Online publication: 05 September 2015
  • Chapter DOI: https://doi.org/10.1017/CBO9781316271889.017
Available formats
×