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MiS Preprint
76/2010

On product structures in Floer homology of cotangent bundles

Alberto Abbondandolo and Matthias Schwarz

Abstract

In an earlier paper we have shown that the pair-of-pants product on the Floer homology of the cotangent bundle of an oriented compact manifold $Q$ corresponds to the Chas-Sullivan loop product on the singular homology of the free loop space of $Q$. We now give chain level constructions of further product structures in Floer homology, corresponding to the cup product on the homology of any path space, and to the Goresky-Hingston product on the relative cohomology of the free loop space modulo constant loops. Moreover, we give a explicit construction for the inverse isomorphism between Floer homology and loop space homology.

Received:
Dec 16, 2010
Published:
Dec 17, 2010
MSC Codes:
53D40, 57R58, 37J45, 37J50
Keywords:
Floer homology, product structures, cotangent bundle

Related publications

inBook
2012 Repository Open Access
Alberto Abbondandolo and Matthias Schwarz

On product structures in Floer homology of cotangent bundles

In: Global differential geometry / Christian Bär... (eds.)
Berlin : Springer, 2012. - pp. 491-521
(Springer proceedings in mathematics ; 17)