The diffeomorphism group of the solid closed torus and Hochschild homology

Abstract

We prove that for a self-injective ribbon Grothendieck-Verdier category C \mathcal {C} in the sense of Boyarchenko-Drinfeld the cyclic action on the Hochschild complex of C \mathcal {C} extends to an action of the diffeomorphism group of the solid closed torus S 1 × D 2 \mathbb {S}^1 \times \mathbb {D}^2 .