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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
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
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/