Lagrangian Rabinowitz Floer homology and twisted cotangent bundles
dc.contributor.author
Merry, Will J.
dc.date.accessioned
2021-05-01T07:40:16Z
dc.date.available
2017-06-10T20:32:35Z
dc.date.available
2021-05-01T07:40:16Z
dc.date.issued
2014-08
dc.identifier.issn
0046-5755
dc.identifier.issn
1572-9168
dc.identifier.other
10.1007/s10711-013-9903-9
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/70886
dc.identifier.doi
10.3929/ethz-b-000070886
dc.description.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.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
Leaf-wise intersections
en_US
dc.subject
Mañé critical value
en_US
dc.subject
Rabinowitz Floer homology
en_US
dc.title
Lagrangian Rabinowitz Floer homology and twisted cotangent bundles
en_US
dc.type
Journal Article
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2013-09-01
ethz.journal.title
Geometriae Dedicata
ethz.journal.volume
171
en_US
ethz.journal.issue
1
en_US
ethz.journal.abbreviated
Geom Dedicata
ethz.pages.start
345
en_US
ethz.pages.end
386
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Dordrecht
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03839 - Biran, Paul I. / Biran, Paul I.
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::03839 - Biran, Paul I. / Biran, Paul I.
ethz.date.deposited
2017-06-10T20:34:35Z
ethz.source
ECIT
ethz.identifier.importid
imp593650ea7ac2e29907
ethz.ecitpid
pub:112308
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2017-07-12T14:22:38Z
ethz.rosetta.lastUpdated
2023-02-06T21:45:50Z
ethz.rosetta.versionExported
true
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