A combinatorial interpretation of the third integral homology of a group
type: Item
instance of: scholarly article
title: A combinatorial interpretation of the third integral homology of a group
zbMATH Open document ID: 0551.20039
DOI: 10.1016/0022-4049(84)90028-8
author: Allan J. Sieradski
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: In this paper the author gives an interpretation of the third integral homology group \(H_ 3(G)\) through the combinatorial aspects of G. The main result is: Theorem: There is a natural isomorphism \(H_ 3(G)\equiv B(X:R)/C(X:R)\) between \(H_ 3(G)\) and the quotient of the group of balanced identities B(X:R) modulo the group of coupled identities C(X:R) for any presentation (X:R) of G. More interesting results are proved in this direction with topological flavor.
reviewed by: Olympia Talelli
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 3877428
zbMATH Keywords: third integral homology group
zbMATH Keywords: balanced identities
zbMATH Keywords: coupled identities
zbMATH Keywords: presentation
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90028-8
OpenAlex ID: W2094642510
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description: scientific article; zbMATH DE number 3877428