Floer theory and reduced cohomology on open manifolds

Yoel Groman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageAmerican English
Pages (from-to)1273-1390
Number of pages118
JournalGeometry and Topology
Volume27
Issue number4
DOIs
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 MSP (Mathematical Sciences Publishers).

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