Abstract
We discuss conditions under which the universal proper G-CW-complex E G can be chosen to be finite dimensional. The methods we use stem from a general construction introduced in [9], involving spaces parameterized by a partially ordered set. In particular we present a construction, which turns a G-CW-complex X in a canonical way into a proper G-CW-complex Pr(X) of the same homotopy type, with control on the dimension of the new space.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Bestvina and G. Mess, The boundary of negatively curved groups, J. Amer. Math. Soc. 4, No. 3 (1991), 469–481.
N. Brady, I. J. Leary and B. E. A. Nucinkis, On algebraic and geometric dimensions for groups with torsion, preprint.
K. S. Brown, Cohomology of Groups, Graduate Texts in Math. vol. 87, Springer, 1982.
K. S. Brown, Groups of virtually finite dimension, in: Homological Group Theory, edited by C. T. C. Wall, London Math. Soc. Lecture Note Ser. vol. 36, Cambridge University Press, 1979, 27–70.
F. Connolly and T. Kozniewski, Finiteness properties of the classifying spaces of proper Γ-actions, J. Pure Appl. Algebra 41 (1986), 17–36.
W. Dicks and P. H. Kropholler, in preparation.
M. J. Dunwoody, Accessibility and groups of cohomological dimension one, Proc. London Math. Soc. 38 (1997), 193–215.
P. H. Kropholler, Hierarchical decompositions,generalized Tate cohomology, and groups of type FP ∞ ,in: (A. Duncan,N. Gilbert, and J. Howie, eds.) Proceedings of the Edinburgh Conference on Geometric Group Theory, 1993,London Math. Soc. Lecture Note Ser. vol. 204, Cambridge University Press, 1995, 190–216.
P. H. Kropholler and G. Mislin, Groups acting on finite dimensional spaces with finite stabilizers, Comment. Math. Heiv. 73 (1998), 122–136.
W. Lück, The type of the classifying space for a family of subgroups, J. Pure Appl. Algebra 149 (2000), 177–203.
U. Stammbach, On the weak (homological) dimension of the group algebra of solvable groups, J. London Math. Soc. (2) 2 (1970), 567–570.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Basel AG
About this paper
Cite this paper
Mislin, G. (2001). On the classifying space for proper actions. In: Aguadé, J., Broto, C., Casacuberta, C. (eds) Cohomological Methods in Homotopy Theory. Progress in Mathematics, vol 196. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8312-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-0348-8312-2_17
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9513-2
Online ISBN: 978-3-0348-8312-2
eBook Packages: Springer Book Archive