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 | |
| 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.