The decomposition of 3-dimensional Poincaré complexes
The decomposition of 3-dimensional Poincaré complexes
We show that if the fundamental group of an orientable PD3-complex has infinitely many ends then it is either a proper free product or virtually free of finite rank. It follows that every PD3-complex is finitely covered by one which is homotopy equivalent to a connected sum of aspherical PD3-complexes and copies of S^1 \times S^2. Furthermore, it is shown that any torsion element of the fundamental group of an orientable PD3-complex has finite centraliser.
poincaré complex, graph of groups, tree
232-246
Crisp, J.
92ec42d1-ff21-49cc-aa99-594a35027009
2000
Crisp, J.
92ec42d1-ff21-49cc-aa99-594a35027009
Crisp, J.
(2000)
The decomposition of 3-dimensional Poincaré complexes.
Commentarii Mathematici Helvetici, 75 (2), .
Abstract
We show that if the fundamental group of an orientable PD3-complex has infinitely many ends then it is either a proper free product or virtually free of finite rank. It follows that every PD3-complex is finitely covered by one which is homotopy equivalent to a connected sum of aspherical PD3-complexes and copies of S^1 \times S^2. Furthermore, it is shown that any torsion element of the fundamental group of an orientable PD3-complex has finite centraliser.
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Published date: 2000
Keywords:
poincaré complex, graph of groups, tree
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Local EPrints ID: 29863
URI: http://eprints.soton.ac.uk/id/eprint/29863
PURE UUID: 10fba9b8-93a7-407f-a197-6ef6b5c528e0
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Date deposited: 19 Mar 2007
Last modified: 08 Jan 2022 12:56
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Author:
J. Crisp
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