Rabinowitz Floer homology for tentacular Hamiltonians

F Pasquotto; R.C.A.M. Van der vorst; Jagna Wisniewska

doi:10.1093/imrn/rnaa132

Rabinowitz Floer homology for tentacular Hamiltonians

F Pasquotto
, R.C.A.M. Van der vorst
, Jagna Wisniewska^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

This paper extends the definition of Rabinowitz Floer homology to non-compact hypersurfaces. We present a general framework for the construction of Rabinowitz Floer homology in the non-compact setting under suitable compactness assumptions on the periodic orbits and the moduli spaces of Floer trajectories. We introduce a class of hypersurfaces arising as the level sets of specific Hamiltonians: strongly tentacular Hamiltonians for which the compactness conditions are satisfied, cf. [ 21], thus enabling us to define the Rabinowitz Floer homology for this class. Rabinowitz Floer homology in turn serves as a tool to address the Weinstein conjecture and establish existence of closed characteristics for non-compact contact manifolds.

Original language	English
Pages (from-to)	2027-2085
Number of pages	59
Journal	International Mathematics Research Notices
Volume	2022
Issue number	3
Early online date	23 Jun 2020
DOIs	https://doi.org/10.1093/imrn/rnaa132
Publication status	Published - Feb 2022

Bibliographical note

Funding Information:
This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) [grant 613.001.111] Periodic motions on non-compact energy surfaces; and by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (SNF) [grant 200021_182564 to J.W.] Periodic orbits on non-compact hypersurfaces.

Publisher Copyright:
© The Author(s) 2020.

Funding

This work was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO) [grant 613.001.111] Periodic motions on non-compact energy surfaces; and by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (SNF) [grant 200021_182564 to J.W.] Periodic orbits on non-compact hypersurfaces.

Funders	Funder number
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung	182564, 200021_182564
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	613.001.111

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title = "Rabinowitz Floer homology for tentacular Hamiltonians",

abstract = "This paper extends the definition of Rabinowitz Floer homology to non-compact hypersurfaces. We present a general framework for the construction of Rabinowitz Floer homology in the non-compact setting under suitable compactness assumptions on the periodic orbits and the moduli spaces of Floer trajectories. We introduce a class of hypersurfaces arising as the level sets of specific Hamiltonians: strongly tentacular Hamiltonians for which the compactness conditions are satisfied, cf. [ 21], thus enabling us to define the Rabinowitz Floer homology for this class. Rabinowitz Floer homology in turn serves as a tool to address the Weinstein conjecture and establish existence of closed characteristics for non-compact contact manifolds.",

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AB - This paper extends the definition of Rabinowitz Floer homology to non-compact hypersurfaces. We present a general framework for the construction of Rabinowitz Floer homology in the non-compact setting under suitable compactness assumptions on the periodic orbits and the moduli spaces of Floer trajectories. We introduce a class of hypersurfaces arising as the level sets of specific Hamiltonians: strongly tentacular Hamiltonians for which the compactness conditions are satisfied, cf. [ 21], thus enabling us to define the Rabinowitz Floer homology for this class. Rabinowitz Floer homology in turn serves as a tool to address the Weinstein conjecture and establish existence of closed characteristics for non-compact contact manifolds.

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Rabinowitz Floer homology for tentacular Hamiltonians

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