Homology, Homotopy and Applications
Volume 6 (2004)
On dimensions in Bredon homology
Pages: 33 – 47
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.
Bredon homology, (co)homological dimension, Hirsch length
2010 Mathematics Subject Classification
18Gxx, 20F18, 20J05, 55N25