Topological Hochschild Homology

Abstract

In the appendix to [20] Waldhausen discussed a trace map tr:K(R)→HH(R), from the algebraic K-theory of a ring to its Hochschild homology, which can be used to obtain information about K(R) from HH(R). In [1] Bökstedt described a factorization of this trace map. The intermediate functor THH(HR) is called the topological Hochschild homology of the Eilenberg–MacLane spectrum HR associated with R, because it is constructed similarly to Hochschild homology with the tensor product replaced by the smash product of spectra.