#### 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
##### 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
 Alberto Abbondandolo Dipartimento di Matematica Universita di Pisa Largo Bruno Pontecorvo 5 56127 Pisa Italy http://www.dm.unipi.it/~abbondandolo/ Matthias Schwarz Universität Leipzig Mathematisches Institut Postfach 10 09 20 D-04009 Leipzig Germany http://www.math.uni-leipzig.de/~schwarz/