The transfer map in topological Hochschild homology

Abstract

We consider the topological Hochschild homology (THH) of a group ring R[ G], and calculate the restriction map (or transfer) associated with a subgroup K ⊆ G of finite index in terms of ordinary group homology transfers. This gives information on the corresponding restriction map in Quillen's K-theory via the topological Dennis trace tr: K( R[ G]) → THH( R[ G]). More generally, we consider group rings for “rings up to homotopy” (FSP's) and calculate the THH-rcstriction map in terms of transfers in generalized homology theories.