On algebraic and geometric dimensions for groups with torsion
On algebraic and geometric dimensions for groups with torsion
We argue that the geometric dimension of a discrete group G ought to be defined to be the minimal dimension of a model for the universal proper G-space rather than the minimal dimension of a model for the universal free G-space. For torsion-free groups, these two quantities are equal, but the new quantity can be finite for groups containing torsion whereas the old one cannot. There is an analogue of cohomological dimension (defined in terms of Bredon cohomology) for which analogues of the Eilenberg-Ganea and Stalling-Swan theorems (due to W. Lueck and M. J. Dunwoody respectively) hold. We show that some groups constructed by M. Bestvina and M. Davis provide counterexamples to the analogue of the Eilenberg-Ganea conjecture.
489-500
Brady, Noel
466bfef1-bc8f-4086-95cf-927148f3ab68
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c
October 2001
Brady, Noel
466bfef1-bc8f-4086-95cf-927148f3ab68
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c
Brady, Noel, Leary, Ian J. and Nucinkis, Brita E.A.
(2001)
On algebraic and geometric dimensions for groups with torsion.
Journal of the London Mathematical Society, 64 (2), .
(doi:10.1112/S002461070100240X).
Abstract
We argue that the geometric dimension of a discrete group G ought to be defined to be the minimal dimension of a model for the universal proper G-space rather than the minimal dimension of a model for the universal free G-space. For torsion-free groups, these two quantities are equal, but the new quantity can be finite for groups containing torsion whereas the old one cannot. There is an analogue of cohomological dimension (defined in terms of Bredon cohomology) for which analogues of the Eilenberg-Ganea and Stalling-Swan theorems (due to W. Lueck and M. J. Dunwoody respectively) hold. We show that some groups constructed by M. Bestvina and M. Davis provide counterexamples to the analogue of the Eilenberg-Ganea conjecture.
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Published date: October 2001
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Local EPrints ID: 29833
URI: http://eprints.soton.ac.uk/id/eprint/29833
ISSN: 0024-6107
PURE UUID: cbeb85c8-353f-4d4e-980f-c29e80c4201b
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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 04:04
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Author:
Noel Brady
Author:
Brita E.A. Nucinkis
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