Product structures in Floer homology

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• Matthias Schwarz, Leipzig
• Wednesday 21 October 2009, 16:00-17:00
• MR 13.

If you have a question about this talk, please contact Jake Rasmussen.

Floer Homology generated by periodic solutions of Hamiltonian systems comes equipped with a natural product structure, the so-called pair-of-pants product. In the case of closed symplectic manifolds this is known to be isomorphic to the quantum cup-product. In the case of noncompact symplectic manifolds such as cotangent bundles, however, Floer homology  becomes a truly infinite dimensional theory and the pair-of-pants product recovers the loop product according to Chas and Sullivan. It will be shown how to construct the classical cup product on loop space cohomology on chain level in Floer homology. Also, the cohomology product according to Goresky and Hingston has a chain level counterpart in Floer homology.  

This talk is part of the Differential Geometry and Topology Seminar series.

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