An Eilenberg-Ganea Phenomenon for Actions with Virtually Cyclic Stabilisers

2012/07/05 by Martin Fluch, Fluch, Martin, Ian J. Leary +1
Mathematics · #20J05 #55N25 #57M20 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20J05 #msc:55N25 #msc:57M20

paper · pdf · doi:10.48550/arxiv.1207.1474

Version 2 is as accepted by Groups, Geometry and Dynamics

arxiv created 2014/04/24 · arxiv updated 2014/04/25

Abstract

In dimension 3 and above, Bredon cohomology gives an acurate purely algebraic description of the minimal dimension of the classifying space for actions of a group with stabilisers in any given family of subgroups. For some Coxeter groups and the family of virtually cyclic subgroups we show that the Bredon cohomological dimension is 2 while the Bredon geometric dimension is 3.

Related

• On Bredon (Co-)Homological Dimensions of Groups
• Bredon cohomological dimensions for groups acting on CAT(0)-spaces
• Bredon cohomological dimension for virtually abelian stabilisers for\n CAT(0) groups
• Intermediaries in Bredon (Co)homology and Classifying Spaces
• Equivariant dimensions of groups with operators