Lagrangian Rabinowitz Floer homology and twisted cotangent bundles
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Date
2014-08
Publication Type
Journal Article
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yes
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Abstract
We study the following rigidity problem in symplectic geometry: can one displace a Lagrangian submanifold from a hypersurface? We relate this to the Arnold Chord Conjecture, and introduce a refined question about the existence of relative leaf-wise intersection points, which are the Lagrangian-theoretic analogue of the notion of leaf-wise intersection points defined by Moser (Acta. Math. 141(1–2):17–34, 1978). Our tool is Lagrangian Rabinowitz Floer homology, which we define first for Liouville domains and exact Lagrangian submanifolds with Legendrian boundary. We then extend this to the ‘virtually contact’ setting. By means of an Abbondandolo–Schwarz short exact sequence we compute the Lagrangian Rabinowitz Floer homology of certain regular level sets of Tonelli Hamiltonians of sufficiently high energy in twisted cotangent bundles, where the Lagrangians are conormal bundles. We deduce that in this situation a generic Hamiltonian diffeomorphism has infinitely many relative leaf-wise intersection points.
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published
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Journal / series
Volume
171 (1)
Pages / Article No.
345 - 386
Publisher
Springer
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Subject
Leaf-wise intersections; Mañé critical value; Rabinowitz Floer homology
Organisational unit
03839 - Biran, Paul I. / Biran, Paul I.
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.