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Floer theory of disjointly supported Hamiltonians on symplectically aspherical manifolds

Yaniv Ganor and Shira Tanny

Algebraic & Geometric Topology 23 (2023) 645–732
Abstract

We study the Floer-theoretic interaction between disjointly supported Hamiltonians by comparing Floer-theoretic invariants of these Hamiltonians with the ones of their sum. These invariants include spectral invariants, boundary depth and Abbondandolo, Haug and Schlenk’s action selector. Additionally, our method shows that in certain situations, the spectral invariants of a Hamiltonian supported in an open subset of a symplectic manifold are independent of the ambient manifold.

Keywords
symplectic geometry, symplectic topology, Floer theory, Floer homology, disjointly supported Hamiltonians, locality in Floer theory, spectral invariants, boundary depth, Schwarz capacity, action selectors, max formula, superheavy sets
Mathematical Subject Classification
Primary: 53D40, 57R17, 57R58
References
Publication
Received: 7 August 2020
Revised: 23 June 2021
Accepted: 22 September 2021
Published: 9 May 2023
Authors
Yaniv Ganor
Department of Mathematics
Technion - Israel Institute of Technology
Haifa
Israel
Shira Tanny
School of Mathematics
Institute for Advanced Study
Princeton, NJ
United States

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