# Classifying Spaces with Virtually Cyclic Stabilisers for Certain Infinite Cyclic Extensions

@article{Fluch2010ClassifyingSW,
title={Classifying Spaces with Virtually Cyclic Stabilisers for Certain Infinite Cyclic Extensions},
author={Martin G. Fluch},
journal={arXiv: Group Theory},
year={2010}
}
• M. Fluch
• Published 7 May 2010
• Mathematics
• arXiv: Group Theory
7 Citations

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## References

SHOWING 1-10 OF 27 REFERENCES
On the classifying space of the family of virtually cyclic subgroups
• Mathematics
• 2007
We study the minimal dimension of the classifying space of the family of virtually cyclic subgroups of a discrete group. We give a complete answer for instance if the group is virtually poly-Z,
Cohomological finiteness conditions in Bredon cohomology
• Mathematics
• 2009
We show that soluble groups G of type Bredon‐FP∞ with respect to the family of all virtually cyclic subgroups of G are always virtually cyclic. In such a group centralizers of elements are of type
The Virtually Cyclic Classifying Space of the Heisenberg Group
• Mathematics
• 2008
We are interested in the relationship between the virtual cohomological dimension (or vcd) of a discrete group Gamma and the smallest possible dimension of a model for the classifying space of Gamma
Survey on Classifying Spaces for Families of Subgroups
We define for a topological group G and a family of subgroups $$\mathcal{F}$$ two versions for the classifying space for the family $$\mathcal{F}$$ , the G-CW-version $$E_\mathcal{F}$$ (G) and
On The Dimension of The Virtually Cyclic Classifying Space of a Crystallographic Group
• Mathematics
• 2006
In this paper we construct a model for the classifying space, BVCG, of a crystallographic group G of rank n relative to the family VC of virtually-cyclic subgroups of G. The model is used to show
On classifying spaces for the family of virtually cyclic subgroups
• Mathematics
• 2006
We construct a model for the universal space for G-actions with virtually cyclic stabilizers for groups G in a class that includes all word-hyperbolic groups. We introduce a notation (a
Isomorphism conjectures in algebraic $K$-theory
• Mathematics
• 1993
duff In this paper we are concerned with the four functors Y., Y3 if, *, and *, which map from the category of topological spaces X to the category diff of Q-spectra. The functor 3*( ) (or ?if ( ))
Constructions of E_{vc} and E_{fbc} for groups acting on CAT(0) spaces
If G is a group acting properly by semisimple isometries on a proper CAT(0) space X, then we build models for the classifying spaces E_{vc} and E_{fbc} under the additional assumption that the action