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An analogue of the torus decomposition theorem for certain Poincaré duality groups

An analogue of the torus decomposition theorem for certain Poincaré duality groups
An analogue of the torus decomposition theorem for certain Poincaré duality groups
It is shown that Poincaré duality groups which satisfy the maximal condition on centralisers have a canonical decomposition as the fundamental group of a finite graph of groups in which the edge groups are polycyclic-by-finite. The results give useful information only when there are large polycyclic subgroups. Since 3-manifolds groups satisfy Max-c, the results provide a purely group theoretic proof of the Torus Decomposion Theorem. In general, fundamental groups of closed aspherical manifolds satisfy Poincaré duality and in fact many of the known examples satisfy Max-c. Thus the results provide a new approach to aspherical manifolds of higher dimensions.
0024-6115
503-529
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4

Kropholler, P.H. (1990) An analogue of the torus decomposition theorem for certain Poincaré duality groups. Proceedings of the London Mathematical Society, 60 (3), 503-529.

Record type: Article

Abstract

It is shown that Poincaré duality groups which satisfy the maximal condition on centralisers have a canonical decomposition as the fundamental group of a finite graph of groups in which the edge groups are polycyclic-by-finite. The results give useful information only when there are large polycyclic subgroups. Since 3-manifolds groups satisfy Max-c, the results provide a purely group theoretic proof of the Torus Decomposion Theorem. In general, fundamental groups of closed aspherical manifolds satisfy Poincaré duality and in fact many of the known examples satisfy Max-c. Thus the results provide a new approach to aspherical manifolds of higher dimensions.

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More information

Published date: 1990
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 349621
URI: https://eprints.soton.ac.uk/id/eprint/349621
ISSN: 0024-6115
PURE UUID: 9c55f9b5-b7ba-443b-b162-42c422bb599c
ORCID for P.H. Kropholler: ORCID iD orcid.org/0000-0001-5460-1512

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Date deposited: 12 Mar 2013 12:19
Last modified: 26 Jul 2019 00:31

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