Geometry & Topology 14 (2010) 1569–1722

DOI: 10.2140/gt.2010.14.1569

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

Primary: 53D40, 57R58

Secondary: 55N45

References

Publication

Received: 6 February 2009
Revised: 6 December 2009
Accepted: 2 May 2010
Published: 1 July 2010
Proposed: Yasha Eliashberg
Seconded: Leonid Polterovich, Ralph Cohen

Authors