On the multiplicative structure of topological Hochschild homology

Abstract

We show that the topological Hochschild homology $THH\left(R\right)$ of an $E_n$–ring spectrum $R$ is an $E_{n-1}$–ring spectrum. The proof is based on the fact that the tensor product of the operad $\mathcal{A}ss$ for monoid structures and the little $n$–cubes operad ${\mathcal{C}}_n$ is an $E_{n+1}$–operad, a result which is of independent interest.