2-Hochschild homology and Frobenius manifolds

Here are transparecies from the Cuban congress. This is a draft note on the same subject.

UPD: The only property of 2-Hochschild homology I explored here is its rigidity. In this post a new rigid functor – spherical homology – appears, that seems to be much more relevant. I hope to discuss the relation between Frobenius  manifolds and spherical homology elsewhere. Until then replace here 2-Hochschild with spherical, please.