Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-15T23:57:00.888Z Has data issue: false hasContentIssue false
  • English
  • Français

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: palbers@math.purdue.edu
AL MOMIN
Affiliation:
Department of Mathematics, Purdue University. e-mail: amomin@math.purdue.edu
Get access Rights & Permissions [Opens in a new window]

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

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

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