| Résume||We have shown that the Khovanov-type homology of links in a thickened annulus, first defined by Asaeda, Przytycki, and Sikora, can be constructed by computing Hochschild homology of bimodules assigned to tangles by Chen and Khovanov. Deforming the Hochschild homology leads to a new, stronger invariant of annular links, which we call the quantum annular homology. In particular, it carries an action of the quantum SL_2, and it assigns a nontrivial polynomial to closed surfaces. In my talk I will describe main points of the construction and then I will discuss a possibility to extend it for links in thickened surfaces other than the annulus.
It is a joint work with Anna Beliakova (University of Zurich) and Stephan Wehrli (Syracuse University)