Splittings of Poincaré duality groups
type: Item
instance of: scholarly article
title: Splittings of Poincaré duality groups
zbMATH Open document ID: 0623.20038
DOI: 10.1007/BF01418340
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183743
review text: If \(G\) is an \(n\)-dimensional Poincaré duality group and \(S\) is an \(n-1\)-dimensional Poincaré duality subgroup then it is quite common for \(G\) to split over \(S\), either as free product with amalgamation, or as an HNN-extension. In this paper we introduce an obstruction \(\text{sing}_G(S)\), in the form of a certain cohomology class. A splitting of \(G\) over a subgroup commensurable with \(S\) exists if and only if this obstruction vanishes. The algebraic theory has close parallels in the theory of aspherical manifolds.
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 57P10
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F34
zbMATH DE Number: 4010781
zbMATH Keywords: Poincaré duality groups
zbMATH Keywords: free products with amalgamation
zbMATH Keywords: HNN-extensions
zbMATH Keywords: cohomology classes
zbMATH Keywords: splittings
zbMATH Keywords: aspherical manifolds
author: Peter H. Kropholler
author: Martin A. Roller
MaRDI profile type: Publication
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OpenAlex ID: W3020855561
description: scientific article; zbMATH DE number 4010781