#### Volume 14, issue 3 (2010)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
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