Nikita Markarian’s mathblog

In the previous post everything is based on the following observation. Let $A$ be an algebra over chains of small discs operad. Then $A$ is in particular a homotopy algebra. I propose that on Hochschild homology of $A$ there is a natural action of an operad equivalent to the
associative operad $Ass$ (this is essentially proved in M. Brun, Z. Fiedorowicz, R. Vogt “On the multiplicative structure of topological Hochschild homology”). More generally, one may try introduce of action (whatever it means) of an operad equivalent to $Ass$ on the category of twisted (semifree) complexes of $A$ and derive the previous action from this one.