Volume 14, issue 3 (2010)

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Floer homology of cotangent bundles and the loop product

Alberto Abbondandolo and Matthias Schwarz

Geometry & Topology 14 (2010) 1569–1722
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.

Keywords
Floer homology, string topology, cotangent bundles, loop product
Mathematical Subject Classification 2000
Primary: 53D40, 57R58
Secondary: 55N45