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Floer homology of
cotangent bundles and the loop product
Alberto Abbondandolo and Matthias Schwarz |
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Geometry & Topology 14 (2010) 1569–1722
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Abstract |
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We prove that the pair-of-pants product on the Floer homology of the cotangent bundle of a compact manifold corresponds to the Chas–Sullivan loop product on the singular homology of the loop space of . 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
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Mathematical Subject Classification 2000
Primary: 53D40, 57R58
Secondary: 55N45
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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
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Authors |
| Alberto Abbondandolo | |
| Dipartimento di Matematica Universita di Pisa Largo Bruno Pontecorvo 5 56127 Pisa Italy |
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| http://www.dm.unipi.it/~abbondandolo/ | |
| Matthias Schwarz | |
| Universität Leipzig Mathematisches Institut Postfach 10 09 20 D-04009 Leipzig Germany |
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| http://www.math.uni-leipzig.de/~schwarz/ | |
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