Corrigendum: "On the Floer homology of cotangent bundles"

TL;DR

This paper corrects an orientation issue in the authors' previous work on Floer homology of cotangent bundles, clarifying the conditions under which the isomorphism with loop space homology holds, especially regarding the second Stiefel-Whitney class.

Contribution

It addresses a crucial orientation correction and extends the isomorphism to cases involving non-vanishing second Stiefel-Whitney class on 2-tori.

Findings

Corrects orientation issues in Floer homology of cotangent bundles

Establishes when twisted Floer complexes are necessary

Clarifies conditions for isomorphism with loop space homology

Abstract

We fix an orientation issue which appears in our previous paper about the isomorphism between Floer homology of cotangent bundles and loop space homology. When the second Stiefel-Whitney class of the underlying manifold does not vanish on 2-tori, this isomorphism requires the use of a twisted version of the Floer complex.