Séminaires : Séminaire d'Algèbre

A Calabi-Yau structure on a smooth algebra allows one to identify Hochschild homology with Hochschild cohomology. With this identification Hochschild homology acquires an additional Gerstenhaber algebra structure. One way to formulate the amount of structure one has on Hochschild homology is to encode it into a 2d TFT. This explains some of the string topology operations on the free loop space of a manifold, but not the string coproduct. If the algebra has additional structure (trivialization of its Hattori-Stalling Euler characteristic) one obtains an extra secondary operation on Hochschild homology, which recovers the string coproduct. Finally, in the free loop space setting, this additional structure can either be recovered from intersection theory of the manifold or from its underlying simple homotopy type, thus relating the two. Using this last relation one can express the difference between the string coproduct of two homotopic but not necessarily homeomorphic manifolds in terms of Whitehead torsion.
This is joint work with Pavel Safronov