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Cup-length estimates for leaf-wise intersections

Published online by Cambridge University Press:  21 July 2010

PETER ALBERS  and
AL MOMIN
PETER ALBERS
Affiliation:
Department of Mathematics, Purdue University. e-mail: [email protected]
AL MOMIN
Affiliation:
Department of Mathematics, Purdue University. e-mail: [email protected]
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Abstract

We prove that on a restricted contact type hypersurface the number of leaf-wise intersections is bounded from below by a certain cup-length.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 3 , November 2010 , pp. 539 - 551
Copyright
Copyright © Cambridge Philosophical Society 2010

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References

REFERENCES

[AF08]Albers, P. and Frauenfelder, U. Infinitely many leaf-wise intersections on cotangent bundles. (2008), arXiv:0812.4426.Google Scholar
[AF10a]Albers, P. and Frauenfelder, U.Leaf-wise intersections and Rabinowitz Floer homology. J. Topol. Anal. 2 (2010), no. 1, 77–98.CrossRefGoogle Scholar
[AF10b]Albers, P. and Frauenfelder, U. On a Theorem by Ekeland-Hofer, arXiv:1001.3386, to appear in Israel J. Math. (2010).Google Scholar
[AF10c]Albers, P. and Frauenfelder, U. Spectral invariants in Rabinowitz Floer homology and global Hamiltonian perturbations. (2010), arXiv:1001.2920.Google Scholar
[AM09]Albers, P. and McLean, M. Non-displaceable contact embeddings and infinitely many leaf-wise intersections, arXiv:0904.3564, to appear in Journal of Symplectic Geometry (2009).Google Scholar
[Ban80]Banyaga, A.On fixed points of symplectic maps. Invent. Math. 56 (1980), no. 3, 215–229.CrossRefGoogle Scholar
[CF09]Cieliebak, K. and Frauenfelder, U.A Floer homology for exact contact embeddings. Pacific J. Math. 293 (2009), no. 2, 251–316.CrossRefGoogle Scholar
[Dra08]Dragnev, D. L.Symplectic rigidity, symplectic fixed points, and global perturbations of Hamiltonian systems. Comm. Pure Appl. Math. 61 (2008), no. 3, 346–370.CrossRefGoogle Scholar
[EH89]Ekeland, I. and Hofer, H.Two symplectic fixed-point theorems with applications to Hamiltonian dynamics. J. Math. Pures Appl. (9) 68 (1989), no. 4, 467–489 (1990).Google Scholar
[Flo89]Floer, A.Cuplength estimates on Lagrangian intersections. Comm. Pure Appl. Math. 42 (1989), no. 4, 335–356.CrossRefGoogle Scholar
[Gin07]Ginzburg, V. L.Coisotropic intersections. Duke Math. J. 140 (2007), no. 1, 111–163.CrossRefGoogle Scholar
[Gür09]Gürel, B. Leafwise Coisotropic Intersections. Int. Math. Res. Not. (2009), article ID rnp 164.CrossRefGoogle Scholar
[Hof88]Hofer, H.Lusternik-Schnirelman-theory for Lagrangian intersections. Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988), no. 5, 465–499.CrossRefGoogle Scholar
[Hof90]Hofer, H.On the topological properties of symplectic maps. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), no. 1–2, 25–38.CrossRefGoogle Scholar
[Kan09]Kang, J. Existence of leafwise intersection points in the unrestricted case. (2009), arXiv:0910.2369.Google Scholar
[Liu05]Liu, C.-G.Cup-length estimate for Lagrangian intersections. J. Differential Equations 209 (2005), no. 1, 57–76.CrossRefGoogle Scholar
[Mer10]Merry, W. On the Rabinowitz Floer homology of twisted cotangent bundles. (2010), arXiv:1002.0162.Google Scholar
[Mos78]Moser, J.A fixed point theorem in symplectic geometry. Acta Math. 141 (1978), no. 1–2, 17–34.CrossRefGoogle Scholar
[MS98]McDuff, D. and Salamon, D. A.Introduction to Symplectic Topology, second ed., Oxford Mathematical Monographs. (The Clarendon Press, Oxford University Press, 1998).Google Scholar
[Sch93]Schwarz, M.Morse homology. Progr. Math. 111 (1993).CrossRefGoogle Scholar
[Sch98]Schwarz, M.A quantum cup-length estimate for symplectic fixed points. Invent. Math. 133 (1998), no. 2, 353–397.CrossRefGoogle Scholar
[Zil08]Ziltener, F. Coisotropic submanifolds, leafwise fixed points, and presymplectic embeddings. arXiv:0811.3715, to appear in Journal of Symplectic Geometry (2008).Google Scholar