Wrapped Floer homology and subcritical handle attachment

TL;DR

This paper discusses the invariance of wrapped Floer homology under subcritical handle attachment, fixing a gap in the existing proof and adapting methods from symplectic homology to clarify the effect of handle attachment.

Contribution

It provides a corrected and detailed proof of the invariance of wrapped Floer homology under subcritical handle attachment, building on and refining previous work.

Findings

Confirmed invariance of wrapped Floer homology under subcritical handle attachment

Fixed a gap in the existing proof regarding Hamiltonian choices

Adapted arguments from Fauck's thesis to the context of Floer homology

Abstract

In this expository article, we present the proof of the invariance of the wrapped Floer homology under the subcritical handle attachment. This is proved by Irie. Here, we fix a minor gap in the proof about the choice of a cofinal family of Hamiltonians. We adapt the arguments from Fauck's PhD thesis, who resolved the gap for the case of handle attachment in symplectic homology. The effect of the handle attachment on the symplectic homology was originally explored by Cieliebak.