On product structures in Floer homology of cotangent bundles

Alberto Abbondandolo and Matthias Schwarz

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Submission date: 16. Dec. 2010
Pages: 20
published in: Global differential geometry / C. Bär ... (eds.)
Berlin : Springer, 2012. - P. 491 - 521
(Springer proceedings in mathematics ; 17) 
DOI number (of the published article): 10.1007/978-3-642-22842-1_16
Bibtex
MSC-Numbers: 53D40, 57R58, 37J45, 37J50
Keywords and phrases: Floer homology, product structures, cotangent bundle
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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.