Some examples of discrete group actions on aspherical manifolds

Some examples of discrete group actions on aspherical manifolds

We construct two classes of examples of virtually torsion-free groups G acting properly cocompactly on contractible manifolds X. In the first class of examples, the universal space for proper actions has no model with finitely many orbits of cells (and so the given manifold X cannot have this equivariant homotopy type). The reason is that the centralizers of some finite subgroups of G do not have finite-type classifying spaces.

In the second class of examples, X is a CAT(0) manifold upon which G acts by isometries, and hence X is a model for the universal space for proper G actions. In these examples, the fixed-point sets for some finite subgroups of G are not manifolds and the centralizers of these subgroups are not virtual Poincare duality groups.

981-238-223-2

139-150

Davis, M.W.

d1f3f122-418d-4217-a490-fa38ae350b01

Leary, I.J.

57bd5c53-cd99-41f9-b02a-4a512d45150e

2003

Davis, M.W.

d1f3f122-418d-4217-a490-fa38ae350b01

Leary, I.J.

57bd5c53-cd99-41f9-b02a-4a512d45150e

Davis, M.W. and Leary, I.J.
(2003)
Some examples of discrete group actions on aspherical manifolds.
Farrell, F.T. and Luck, W.
(eds.)
In *High-Dimensional Manifold Topology: Proceedings of the School Ictp. *
World Scientific.
.
(doi:10.1142/9789812704443_0006).

Record type:
Conference or Workshop Item
(Paper)

## Abstract

We construct two classes of examples of virtually torsion-free groups G acting properly cocompactly on contractible manifolds X. In the first class of examples, the universal space for proper actions has no model with finitely many orbits of cells (and so the given manifold X cannot have this equivariant homotopy type). The reason is that the centralizers of some finite subgroups of G do not have finite-type classifying spaces.

In the second class of examples, X is a CAT(0) manifold upon which G acts by isometries, and hence X is a model for the universal space for proper G actions. In these examples, the fixed-point sets for some finite subgroups of G are not manifolds and the centralizers of these subgroups are not virtual Poincare duality groups.

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## More information

Published date: 2003

Venue - Dates:
School on High-Dimensional Manifold Topology 2001 ICTP Trieste, Trieste, Italy, 2001-05-21 - 2001-06-08

Organisations:
Pure Mathematics

## Identifiers

Local EPrints ID: 199381

URI: http://eprints.soton.ac.uk/id/eprint/199381

ISBN: 981-238-223-2

PURE UUID: 42c19ff6-9053-4d37-b844-d9a2e9b0ce14

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Date deposited: 18 Oct 2011 14:38

Last modified: 15 Mar 2024 03:36

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## Contributors

Author:
M.W. Davis

Editor:
F.T. Farrell

Editor:
W. Luck

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