Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-09T19:48:24.644Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  06 March 2020

Chris Wendl
Chris Wendl
Affiliation:
Humboldt-Universität zu Berlin
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory , pp. 177 - 181
Publisher: Cambridge University Press
Print publication year: 2020

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

Abbas, C., Holomorphic open book decompositions, Duke Math. J. 158 (2011), no. 1, 29–82.Google Scholar
Abbas, C., Cieliebak, K., and , H., The Weinstein conjecture for planar contact structures in dimension three, Comment. Math. Helv. 80 (2005), no. 4, 771–793.Google Scholar
Adams, R. A. and Fournier, J. J. F., Sobolev Spaces, 2nd ed., Pure and Applied Mathematics (Amsterdam), vol. 140, Elsevier/Academic Press, Amsterdam, 2003.Google Scholar
Akhmedov, A., Etnyre, J. B., Mark, T. E., and Smith, I., A note on Stein fillings of contact manifolds, Math. Res. Lett. 15 (2008), no. 6, 1127–1132.Google Scholar
Audin, M. and Damian, M., Morse Theory and Floer Homology, Universitext, Springer, London; EDP Sciences, Les Ulis, 2014. Translated from the 2010 French original by Reinie Erné.Google Scholar
Baker, K. L., Etnyre, J. B., and Van Horn-Morris, J., Cabling, contact structures and mapping class monoids, J. Differ. Geom. 90 (2012), no. 1, 1–80.Google Scholar
Borman, M. S., Eliashberg, Y., and Murphy, E., Existence and classification of overtwisted contact structures in all dimensions, Acta Math. 215 (2015), no. 2, 281–361.Google Scholar
Bourgeois, F., A Morse–Bott approach to contact homology, Ph.D. Thesis, Stanford University, 2002.Google Scholar
Bourgeois, F., Contact homology and homotopy groups of the space of contact structures, Math. Res. Lett. 13 (2006), no. 1, 71–85.Google Scholar
Bourgeois, F., Eliashberg, Y., Hofer, H., Wysocki, K., and Zehnder, E., Compactness results in symplectic field theory, Geom. Topol. 7 (2003), 799–888.Google Scholar
Bourgeois, F. and Mohnke, K., Coherent orientations in symplectic field theory, Math. Z. 248 (2004), no. 1, 123–146.Google Scholar
Bredon, G. E., Topology and Geometry, Springer-Verlag, New York, 1993.CrossRefGoogle Scholar
Cieliebak, K. and Eliashberg, Y., From Stein to Weinstein and Back: Symplectic Geometry of Affine Complex Manifolds, American Mathematical Society Colloquium Publications, vol. 59, American Mathematical Society, Providence, RI, 2012.Google Scholar
Cioba, A. and Wendl, C., Unknotted Reeb orbits and nicely embedded holomorphic curves. Preprint arXiv:1609.01660, to appear in J. Symplect. Geom.Google Scholar
Conley, C. and Zehnder, E., An Index Theory for Periodic Solutions of a Hamiltonian System, Geometric dynamics (Rio de Janeiro, 1981), Lecture Notes in Mathematics, vol. 1007, Springer, Berlin, 1983, pp. 132–145.Google Scholar
Conway, J. and Etnyre, J. B., Contact surgery and symplectic caps. Preprint arXiv:1811.00387.Google Scholar
Donaldson, S. K., Lefschetz pencils on symplectic manifolds, J. Differ. Geom. 53 (1999), no. 2, 205–236.Google Scholar
Dragnev, D. L., Fredholm theory and transversality for noncompact pseudoholomorphic maps in symplectizations, Comm. Pure Appl. Math. 57 (2004), no. 6, 726–763.Google Scholar
Eliashberg, Y., Classification of overtwisted contact structures on 3-manifolds, Invent. Math. 98 (1989), no. 3, 623–637.Google Scholar
Eliashberg, Y., Filling by Holomorphic Discs and Its Applications, Geometry of low-dimensional manifolds, 2 (Durham, 1989), London Mathematical Society Lecture Note Series, vol. 151, Cambridge University Press, Cambridge, 1990, pp. 45–67.Google Scholar
Eliashberg, Y., On symplectic manifolds with some contact properties, J. Differ. Geom. 33 (1991), no. 1, 233–238.Google Scholar
Eliashberg, Y., Givental, A., and Hofer, H., Introduction to symplectic field theory, Geom. Funct. Anal., Special Volume (2000), 560–673.CrossRefGoogle Scholar
Eliashberg, Y. and Murphy, E., Making cobordisms symplectic. Preprint arXiv:1504.06312.Google Scholar
Etnyre, J. B., Symplectic convexity in low-dimensional topology, Topology Appl. 88 (1998), no. 1–2, 3–25. Symplectic, contact and low-dimensional topology (Athens, GA, 1996).Google Scholar
Etnyre, J. B., Planar open book decompositions and contact structures, Int. Math. Res. Not. 79 (2004), 4255–4267.Google Scholar
Etnyre, J. B., Lectures on Open Book Decompositions and Contact Structures, Floer homology, gauge theory, and low-dimensional topology, Clay Mathematics Proceedings, vol. 5, American Mathematical Society, Providence, RI, 2006, pp. 103–141.Google Scholar
Etnyre, J. B. and Honda, K., On the nonexistence of tight contact structures, Ann. of Math. (2) 153 (2001), no. 3, 749–766.Google Scholar
Etnyre, J. B. and Honda, K., On symplectic cobordisms, Math. Ann. 323 (2002), no. 1, 31–39.Google Scholar
Evans, L. C., Partial Differential Equations, Graduate Studies in Mathematics, vol. 19, American Mathematical Society, Providence, RI, 1998.Google Scholar
Geiges, H., An Introduction to Contact Topology, Cambridge Studies in Advanced Mathematics, vol. 109, Cambridge University Press, Cambridge, 2008.Google Scholar
Ghiggini, P., Strongly fillable contact 3-manifolds without Stein fillings, Geom. Topol. 9 (2005), 1677–1687.Google Scholar
Giroux, E., Géométrie de contact: de la dimension trois vers les dimensions supérieures, Proceedings of the International Congress of Mathematicians, vol. 2 (Beijing, 2002), 2002, pp. 405–414.Google Scholar
Gompf, R. E. and Stipsicz, A. I., 4-Manifolds and Kirby Calculus, Graduate Studies in Mathematics, vol. 20, American Mathematical Society, Providence, RI, 1999.Google Scholar
Gromov, M., Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347.Google Scholar
Hind, R., Holomorphic filling of RP3, Commun. Contemp. Math. 2 (2000), no. 3, 349–363.Google Scholar
Hind, R., Stein fillings of lens spaces, Commun. Contemp. Math. 5 (2003), no. 6, 967–982.Google Scholar
Hirsch, M. W., Differential Topology, Springer-Verlag, New York, 1994.Google Scholar
Hofer, H., Lizan, V., and Sikorav, J.-C., On genericity for holomorphic curves in four-dimensional almost-complex manifolds, J. Geom. Anal. 7 (1997), no. 1, 149–159.Google Scholar
Hofer, H., Wysocki, K., and Zehnder, E., Properties of pseudo-holomorphic curves in symplectisations. II. Embedding controls and algebraic invariants, Geom. Funct. Anal. 5 (1995), no. 2, 270–328.Google Scholar
Hofer, H., Wysocki, K., and Zehnder, E., Properties of pseudoholomorphic curves in symplectisations. I. Asymptotics, Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996), no. 3, 337–379.Google Scholar
Hofer, H., Wysocki, K., and Zehnder, E., Properties of Pseudoholomorphic Curves in Symplectisations. IV. Asymptotics with Degeneracies, Contact and Symplectic Geometry (Cambridge, 1994), Cambridge University Press, Cambridge, 1996, pp. 78–117.Google Scholar
Hofer, H., Wysocki, K., and Zehnder, E., Properties of pseudoholomorphic curves in symplectizations. III. Fredholm theory, Top. Nonlin. Anal. 13 (1999), 381–475.Google Scholar
Hofer, H. and Zehnder, E., Symplectic Invariants and Hamiltonian Dynamics, Birkhäuser Verlag, Basel, 1994.Google Scholar
Hryniewicz, U., Fast finite-energy planes in symplectizations and applications, Trans. Amer. Math. Soc. 364 (2012), no. 4, 1859–1931.Google Scholar
Hryniewicz, U., Momin, A., and Salomão, P. A. S., A Poincaré-Birkhoff theorem for tight Reeb flows on S3, Invent. Math. 199 (2015), no. 2, 333–422.Google Scholar
Hutchings, M., An index inequality for embedded pseudoholomorphic curves in symplectizations, J. Eur. Math. Soc. (JEMS) 4 (2002), no. 4, 313– 361.Google Scholar
Hutchings, M., Lecture Notes on Embedded Contact Homology, Contact and Symplectic Topology, Bolyai Society Mathematical Studies, vol. 26, Springer, New York, 2014, pp. 389–484.Google Scholar
Ivashkovich, S. and Shevchishin, V., Structure of the moduli space in a neighborhood of a cusp-curve and meromorphic hulls, Invent. Math. 136 (1999), no. 3, 571–602.Google Scholar
Kaloti, A. and Li, Y., Stein fillings of contact 3-manifolds obtained as Legendrian surgeries, J. Symplect. Geom. 14 (2016), no. 1, 119–147.Google Scholar
Kriener, M., Intersection formula for finite energy half cylinders, Ph.D. Thesis, ETH Zürich, 1998.Google Scholar
Lalonde, F. and McDuff, D., J-Curves and the Classification of Rational and Ruled Symplectic 4-Manifolds, Contact and Symplectic Geometry (Cambridge, 1994), Cambridge University Press, Cambridge, 1996, pp. 3–42.Google Scholar
Lazarev, O., Maximal contact and symplectic structures. Preprint arXiv:1810.11728.Google Scholar
Lieb, E. H. and Loss, M., Analysis, 2nd ed., Graduate Studies in Mathematics, vol. 14, American Mathematical Society, Providence, RI, 2001.Google Scholar
Lisca, P., Symplectic fillings and positive scalar curvature, Geom. Topol. 2 (1998), 103–116.Google Scholar
Lisca, P., On symplectic fillings of lens spaces, Trans. Amer. Math. Soc. 360 (2008), no. 2, 765–799.Google Scholar
Lisi, S., Van Horn-Morris, J., and Wendl, C., On symplectic fillings of spinal open book decompositions I: Geometric constructions. Preprint arXiv:1810.12017.Google Scholar
Lisi, S., Van Horn-Morris, J., and Wendl, C., On symplectic fillings of spinal open book decompositions II: Holomorphic curves and classification. In preparation.Google Scholar
Martinet, J., Formes de contact sur les variétés de dimension 3, Proceedings of Liverpool Singularities Symposium, II (1969/1970), Springer, Berlin, 1971, pp. 142–163. Lecture Notes in Mathematics, vol. 209 (French).Google Scholar
McDuff, D., The structure of rational and ruled symplectic 4-manifolds, J. Amer. Math. Soc. 3 (1990), no. 3, 679–712.Google Scholar
McDuff, D., Singularities and Positivity of Intersections of J-Holomorphic Curves, Holomorphic curves in symplectic geometry, Progress in Mathematics, vol. 117, Birkhäuser, Basel, 1994, pp. 191–215. With an appendix by Gang Liu.Google Scholar
McDuff, D. and Salamon, D., J-Holomorphic Curves and Symplectic Topology, 2nd ed., American Mathematical Society Colloquium Publications, vol. 52, American Mathematical Society, Providence, RI, 2012.Google Scholar
McDuff, D. and Salamon, D., Introduction to Symplectic Topology, 3rd ed., Oxford University Press, Oxford, 2017.Google Scholar
Micallef, M. J. and White, B., The structure of branch points in minimal surfaces and in pseudoholomorphic curves, Ann. Math. (2) 141 (1995), no. 1, 35–85.Google Scholar
Milnor, J. W., Topology from the Differentiable Viewpoint, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Based on notes by David, W. Weaver; revised reprint of the 1965 original.Google Scholar
Mora, E., Pseudoholomorphic cylinders in symplectisations, Ph.D. Thesis, New York University, 2003.Google Scholar
Niederkrüger, K. and Wendl, C., Weak symplectic fillings and holomorphic curves, Ann. Sci. École Norm. Sup. (4) 44 (2011), no. 5, 801–853.Google Scholar
Ozbagci, B. and Stipsicz, A. I., Surgery on Contact 3-Manifolds and Stein Surfaces, Bolyai Society Mathematical Studies, vol. 13, Springer-Verlag, Berlin, 2004.Google Scholar
Ozbagci, B. and Stipsicz, A. I., Contact 3-manifolds with infinitely many Stein fillings, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1549–1558.Google Scholar
Plamenevskaya, O. and Van Horn-Morris, J., Planar open books, monodromy factorizations and Stein fillings, Geom. Topol. 14 (2010), 2077– 2101.Google Scholar
Salamon, D., Lectures on Floer Homology, Symplectic Geometry and Topology (Park City, UT, 1997), IAS/Park City Mathematics Series, vol. 7, American Mathematical Society, Providence, RI, 1999, pp. 143–229.Google Scholar
Salamon, D. and Zehnder, E., Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992), no. 10, 1303–1360.Google Scholar
Sard, A., The measure of the critical values of differentiable maps, Bull. Amer. Math. Soc. 48 (1942), 883–890.Google Scholar
Schwarz, M., Morse Homology, Progress in Mathematics, vol. 111, Birkhäuser Verlag, Basel, 1993.Google Scholar
Siefring, R., Intersection theory of finite energy surfaces, Ph.D. Thesis, New York University, 2005.Google Scholar
Siefring, R., Relative asymptotic behavior of pseudoholomorphic halfcylinders, Comm. Pure Appl. Math. 61 (2008), no. 12, 1631–1684.Google Scholar
Siefring, R., Intersection theory of punctured pseudoholomorphic curves, Geom. Topol. 15 (2011), 2351–2457.Google Scholar
Siefring, R. and Wendl, C., Pseudoholomorphic curves, intersections and Morse–Bott asymptotics. In preparation.Google Scholar
Sikorav, J.-C., Some Properties of Holomorphic Curves in almost Complex Manifolds, Holomorphic Curves in Symplectic Geometry, Progress in Mathematics, vol. 117, Birkhäuser, Basel, 1994, pp. 165–189.Google Scholar
Sikorav, J.-C., Singularities of J-holomorphic curves, Math. Z. 226 (1997), no. 3, 359–373.Google Scholar
Smith, I., Torus fibrations on symplectic four-manifolds, Turkish J. Math. 25 (2001), no. 1, 69–95.Google Scholar
Thurston, W. P., Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976), no. 2, 467–468.Google Scholar
Thurston, W. P. and Winkelnkemper, H. E., On the existence of contact forms, Proc. Amer. Math. Soc. 52 (1975), 345–347.Google Scholar
Wand, A., Mapping class group relations, Stein fillings, and planar open book decompositions, J. Topol. 5 (2012), no. 1, 1–14.Google Scholar
Wand, A., Factorizations of diffeomorphisms of compact surfaces with boundary, Geom. Topol. 19 (2015), no. 5, 2407–2464.Google Scholar
Wendl, C., Automatic transversality and orbifolds of punctured holomorphic curves in dimension four, Comment. Math. Helv. 85 (2010), no. 2, 347–407.Google Scholar
Wendl, C., Strongly fillable contact manifolds and J-holomorphic foliations, Duke Math. J. 151 (2010), no. 3, 337–384.Google Scholar
Wendl, C., Open book decompositions and stable Hamiltonian structures, Expos. Math. 28 (2010), no. 2, 187–199.Google Scholar
Wendl, C., Lectures on Holomorphic Curves in Symplectic and Contact Geometry. Preprint arXiv:1011.1690.Google Scholar
Wendl, C., Lectures on Symplectic Field Theory. Preprint arXiv:1612.01009, to appear in EMS Series of Lectures in Mathematics.Google Scholar
Wendl, C., Holomorphic Curves in Low Dimensions: From Symplectic Ruled Surfaces to Planar Contact Manifolds, Lecture Notes in Mathematics, vol. 2216, Springer-Verlag, Berlin, 2018.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
  • Chris Wendl, Humboldt-Universität zu Berlin
  • Book: Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
  • Online publication: 06 March 2020
  • Chapter DOI: https://doi.org/10.1017/9781108608954.011
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
  • Chris Wendl, Humboldt-Universität zu Berlin
  • Book: Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
  • Online publication: 06 March 2020
  • Chapter DOI: https://doi.org/10.1017/9781108608954.011
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
  • Chris Wendl, Humboldt-Universität zu Berlin
  • Book: Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory
  • Online publication: 06 March 2020
  • Chapter DOI: https://doi.org/10.1017/9781108608954.011
Available formats
×