On bounded cohomology of amalgamated products of groups.
type: Item
instance of: scholarly article
title: On bounded cohomology of amalgamated products of groups.
zbMATH Open document ID: 1081.20060
DOI: 10.1155/S0161171204311142
author: Igor V. Erovenko
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/52079
review text: In this interesting paper the author investigates the structure of the singular part of the second bounded cohomology group, \(H^2 _{b,2}(G)\), with coefficients in the additive group of reals \(\mathbb{R}\) with trivial action, when \(G\) is an amalgamated product of groups. \(H^2_{b,2}(G)\cong PX(G)/X(G)\), as vector spaces, where \(X(G)\) is the space of additive characters \(G\to\mathbb{R}\) and \(PX(G)\) is the space of pseudocharacters. In certain cases, the author constructs an analog of the initial segment of the Mayer-Vietoris exact cohomology sequence for the spaces of pseudocharacters.
reviewed by: Olympia Talelli
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 2171575
zbMATH Keywords: bounded cohomology
zbMATH Keywords: quasicharacters
zbMATH Keywords: pseudocharacters
zbMATH Keywords: Mayer-Vietoris sequences
MaRDI profile type: Publication
OpenAlex ID: W2159217845
description: scientific article; zbMATH DE number 2171575