Extensions of complexes of groups
type: Item
instance of: scholarly article
title: Extensions of complexes of groups
zbMATH Open document ID: 0762.20018
author: André Haefliger
publication date: 1993-02-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74954
review text: Complexes of groups \(G(X)\) over ordered simplicial complexes \(X\) are generalizations to higher dimensions of graphs of groups. We first relate them to complexes of spaces by considering their classifying space \(BG(X)\). Then we develop their homological algebra aspects. We define the notions of homology and cohomology of a complex of groups \(G(X)\) with coefficients in a \(G(X)\)-module and show the existence of free resolutions. We apply those notions to study extensions of complexes of groups with constant or abelian kernel.
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20E22
Mathematics Subject Classification ID: 57Q05
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F34
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 118268
zbMATH Keywords: ordered simplicial complexes
zbMATH Keywords: graphs of groups
zbMATH Keywords: classifying space
zbMATH Keywords: free resolutions
zbMATH Keywords: extensions of complexes of groups
MaRDI profile type: Publication
OpenAlex ID: W2086326407
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DOI: 10.5802/AIF.1292
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published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 118268