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On product structures in Floer homology of cotangent bundles
Alberto Abbondandolo and Matthias Schwarz
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.