Wrapped Floer homology and subcritical handle attachment

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.