Theory of bounded groups and their bounded cohomology
type: Item
instance of: scholarly article
title: Theory of bounded groups and their bounded cohomology
zbMATH Open document ID: 0616.55002
author: D. W. Paul
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Bounded cohomology H can be defined for groups and for topological spaces. Recent work has shown that \(H^ *_ b(M)\) of a topological space M depends only on \(\pi _ 1(M)\). In this paper we consider a new concept - a bounded group - and thereby expand the definition of bounded cohomology. We prove that bounded cohomology groups are themselves bounded groups and develop their properties in lower dimensions. In particular, elements of \(H^ 2_ b(G,A)\) classify bounded group extensions of G by A. As an application of the theory of bounded groups we construct the Lyndon spectral sequence and obtain a result relating the bounded cohomology of a group and its subgroup.
Mathematics Subject Classification ID: 55N35
Mathematics Subject Classification ID: 20J99
Mathematics Subject Classification ID: 55T99
Mathematics Subject Classification ID: 20E22
zbMATH DE Number: 3998762
zbMATH Keywords: bounded cohomology
zbMATH Keywords: bounded group
zbMATH Keywords: bounded group extensions
zbMATH Keywords: Lyndon spectral sequence
zbMATH Keywords: fundamental group
MaRDI profile type: Publication
full work available at URL: pjm.1988.134.313
OpenAlex ID: W2094021721
DOI: 10.2140/PJM.1988.134.313
description: scientific article; zbMATH DE number 3998762