Title: An Analogue of the Torus Decomposition Theorem for Certain Poincaré Duality Groups
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 group...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 grouptheoretic 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.Read More
Publication Year: 1990
Publication Date: 1990-05-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 56
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot