Relative measure homology and continuous bounded cohomology of topological pairs
type: Item
instance of: scholarly article
title: Relative measure homology and continuous bounded cohomology of topological pairs
zbMATH Open document ID: 1252.55001
author: Roberto Frigerio
author: Cristina Pagliantini
published in: Pacific Journal of Mathematics
publication date: 2012-08-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/1105.4851
full work available at URL: p06.xhtml
review text: In order to exploit measure theory as a tool for computing the simplicial volume, one has to show that several homology theories are not only isomorphic, but also isometric (with respect to some appropriate seminorms). This paper is devoted to extending a result by \textit{C. Löh} [Math. Z. 253, No. 1, 197--218 (2006; Zbl 1093.55004)] to the context of relative homology of topological pairs. First, the authors develop some aspects of the theory of continuous bounded cohomology of topological pairs. They compare this theory with the usual bounded cohomology of pairs of groups and spaces. They show that the seminorm considered in the present paper does not coincide with the seminorm used by \textit{H. Park} [Topology Appl. 131, No. 3, 203--234 (2003; Zbl 1042.55003)] in order to provide the algebraic foundations to the theory of relative bounded cohomology. Finally, they show that Park and Gromov seminorms do not coincide in general.
reviewed by: Vasile Oproiu
Mathematics Subject Classification ID: 55N10
Mathematics Subject Classification ID: 55N33
Mathematics Subject Classification ID: 55U15
Mathematics Subject Classification ID: 53C65
Mathematics Subject Classification ID: 57N65
zbMATH DE Number: 6064445
zbMATH Keywords: simplicial volume
zbMATH Keywords: singular homology
zbMATH Keywords: bounded cohomology of groups
zbMATH Keywords: \(CAT(0)\) spaces
MaRDI profile type: Publication
OpenAlex ID: W2044995088
arXiv ID: 1105.4851
DOI: 10.2140/PJM.2012.257.91
description: scientific article; zbMATH DE number 6064445