Symplectic cohomology and loop homology

Symplectic cohomology and loop homology

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Mohammed Abouzaid, Columbia University
Fine Hall 322

The string topology of Chas-Sullivan produces operations on the homology of the free loop space of orientable manifolds, and analogous structures are known to exist on the symplectic cohomology of their cotangent bundles. Work of Kragh has shown that these groups are only isomorphic under the assumption that the manifold is Spin. The goal of this talk is to define twisted versions of loop space homology and symplectic cohomology for an arbitrary closed, smooth manifold, which are isomorphic to each other. I will also explain how to build Batalin Vilkovisky structures on the two sides which are isomorphic.