#### Volume 7, issue 4 (2007)

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On the multiplicative structure of topological Hochschild homology

### Morten Brun, Zbigniew Fiedorowicz and Rainer M Vogt

Algebraic & Geometric Topology 7 (2007) 1633–1650
 arXiv: math/0410367
##### 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 $\mathsc{A}ss$ for monoid structures and the little $n$–cubes operad ${\mathsc{C}}_{n}$ is an ${E}_{n+1}$–operad, a result which is of independent interest.

Primary: 55P43
Secondary: 18D50
##### Publication
Revised: 10 September 2007
Accepted: 1 October 2007
Published: 17 December 2007
##### Authors
 Morten Brun Department of Mathematics University of Bergen Johs. Brunsgt. 12 N-5008 Bergen Norway http://www.uib.no/People/mbr085/ Zbigniew Fiedorowicz Department of Mathematics The Ohio State University Columbus OH 43210-1174 USA http://www.math.ohio-state.edu/people/fiedorow/view Rainer M Vogt Universität Osnabrück Fachbereich Mathematik/Informatik Albrechtstr. 28a 49069 Osnabrück Germany http://www.mathematik.uni-osnabrueck.de/staff/phpages/vogtr.rdf.shtml