#### Volume 8, issue 2 (2008)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Hochschild homology relative to a family of groups

### Andrew Nicas and David Rosenthal

Algebraic & Geometric Topology 8 (2008) 693–728
##### Abstract

We define the Hochschild homology groups of a group ring $ℤG$ relative to a family of subgroups $\mathsc{ℱ}$ of $G$. These groups are the homology groups of a space which can be described as a homotopy colimit, or as a configuration space, or, in the case $\mathsc{ℱ}$ is the family of finite subgroups of $G$, as a space constructed from stratum preserving paths. An explicit calculation is made in the case $G$ is the infinite dihedral group.

##### Keywords
Hochschild homology, family of subgroups, classifying space
##### Mathematical Subject Classification 2000
Primary: 16E40, 55R35, 19D55
##### Publication
Received: 19 September 2007
Revised: 31 January 2008
Accepted: 12 February 2008
Published: 25 May 2008
##### Authors
 Andrew Nicas Dept. of Mathematics & Statistics McMaster University Hamilton, ON L8S 4K1 Canada David Rosenthal Dept. of Mathematics & Comp. Sci. St. John’s University 8000 Utopia Pkwy Jamaica, NY 11439 USA