Floer theory of disjointly supported Hamiltonians on symplectically aspherical manifolds

TL;DR

This paper investigates how Floer-theoretic invariants behave for disjointly supported Hamiltonians on symplectically aspherical manifolds, revealing their relationships and independence properties.

Contribution

It introduces a method to compare Floer invariants of disjoint Hamiltonians with their sum and shows invariants' independence from the ambient manifold in specific cases.

Findings

Floer invariants of disjoint Hamiltonians relate to those of their sum

Spectral invariants can be independent of the ambient manifold in certain situations

The approach applies to spectral invariants, boundary depth, and action selectors

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-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.