Homology, Homotopy and Applications

Volume 6 (2004)

Number 1

On dimensions in Bredon homology

Pages: 33 – 47

DOI: https://dx.doi.org/10.4310/HHA.2004.v6.n1.a4

Author

Brita E. A. Nucinkis (Departement Mathematik, ETH-Zentrum, Zürich, Switzerland)

Abstract

We define a homological and cohomological dimension of groups in the context of Bredon homology and compare the two quantities. We apply this to describe the Bredon-homological dimension of nilpotent groups in terms of the Hirsch-rank. In particular this implies that for virtually torsion-free nilpotent groups the Bredon cohomological dimension is equal to the virtual cohomological dimension.

Keywords

Bredon homology, (co)homological dimension, Hirsch length

2010 Mathematics Subject Classification

18Gxx, 20F18, 20J05, 55N25

Published 1 January 2004