Homology, Homotopy and Applications

Volume 6 (2004)

Number 1

On dimensions in Bredon homology

Pages: 33 – 47

DOI: http://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

Full Text (PDF format)