Floer theory and reduced cohomology on open manifolds

Groman, Yoel

doi:10.2140/gt.2023.27.1273

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Floer theory and reduced cohomology on open manifolds

Yoel Groman

Geometry & Topology 27 (2023) 1273–1390

DOI: 10.2140/gt.2023.27.1273

Abstract

We construct Hamiltonian Floer complexes associated to continuous, and even lower semicontinuous, time-dependent exhaustion functions on geometrically bounded symplectic manifolds. We further construct functorial continuation maps associated to monotone homotopies between them, and operations which give rise to a product and unit. The work rests on novel techniques for energy confinement of Floer solutions as well as on methods of non-Archimedean analysis. The definition for general Hamiltonians utilizes the notion of reduced cohomology familiar from Riemannian geometry, and the continuity properties of Floer cohomology. This gives rise, in particular, to local Floer theory. We discuss various functorial properties as well as some applications to existence of periodic orbits and to displaceability.

Keywords

symplectic cohomology, geometrically bounded manifolds, tame symplectic manifolds

Mathematical Subject Classification 2010

Primary: 53D40

Secondary: 32P05

References

Publication

Received: 20 September 2017

Revised: 2 November 2021

Accepted: 30 November 2021

Published: 15 June 2023

Proposed: Yakov Eliashberg

Seconded: Leonid Polterovich, Gang Tian

Authors

Yoel Groman
Einstein Institute of Mathematics The Hebrew University of Jerusalem - Givat Ram Jerusalem Israel

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Volume 27, issue 4 (2023)