Floer homology of cotangent bundles and the loop product

Abstract

We prove that the pair-of-pants product on the Floer homology of the cotangent bundle of a compact manifold M corresponds to the Chas-Sullivan loop product on the singular homology of the loop space of M . We also prove related results concerning the Floer homological interpretation of the Pontrjagin product and of the Serre fibration. The techniques include a Fredholm theory for Cauchy-Riemann operators with jumping Lagrangian boundary conditions of conormal type, and a new cobordism argument replacing the standard gluing technique.

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Cite this paper

@inproceedings{Abbondandolo2009FloerHO, title={Floer homology of cotangent bundles and the loop product}, author={Alberto Abbondandolo and Matthias Schwarz}, year={2009} }