Every CW-complex is a classifying space for proper bundles
Every CW-complex is a classifying space for proper bundles
We prove that, up to homotopy equivalence, every connected CW-complex is the quotient of a contractible complex by a proper action of a discrete group, and that every CW-complex is the quotient of an aspherical complex by an action of a group of order two. These results may be viewed as analogues of the Kan-Thurston theorem, in which the universal free G-space has been replaced by the universal proper G-space. The fact that our result concerns homotopy type (whereas the Kan-Thurston theorem concerns homology) is a reflection of the existence of 'contractible groups', i.e., groups for which the quotient of the universal proper G-space by G is contractible.
CW-complex, homotopy type, actions of discrete groups
539-550
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c
2001
Leary, Ian J.
57bd5c53-cd99-41f9-b02a-4a512d45150e
Nucinkis, Brita E.A.
0b1c337c-36ae-4ef3-add4-b49a7c23810c
Abstract
We prove that, up to homotopy equivalence, every connected CW-complex is the quotient of a contractible complex by a proper action of a discrete group, and that every CW-complex is the quotient of an aspherical complex by an action of a group of order two. These results may be viewed as analogues of the Kan-Thurston theorem, in which the universal free G-space has been replaced by the universal proper G-space. The fact that our result concerns homotopy type (whereas the Kan-Thurston theorem concerns homology) is a reflection of the existence of 'contractible groups', i.e., groups for which the quotient of the universal proper G-space by G is contractible.
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Published date: 2001
Keywords:
CW-complex, homotopy type, actions of discrete groups
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Local EPrints ID: 29834
URI: http://eprints.soton.ac.uk/id/eprint/29834
ISSN: 0040-9383
PURE UUID: b6e3ea5c-c4f6-413e-bc55-ff8201a21b60
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Date deposited: 11 May 2006
Last modified: 16 Mar 2024 04:04
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Author:
Brita E.A. Nucinkis
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