Projective resolutions up to bounded torsion and bounds for the orders of the finite subgroups.
type: Item
instance of: scholarly article
title: Projective resolutions up to bounded torsion and bounds for the orders of the finite subgroups.
zbMATH Open document ID: 1311.20050
author: Conchita Martínez-Pérez
author: Julia Ponce Guajardo
published in: Archiv der Mathematik
publication date: 2013-12-23T00:00:00Z
review text: Following the paper by \textit{W. Lück} et al., [K-Theory 30, No. 2, 137-165 (2003; Zbl 1053.55004)], an almost-isomorphism of groups is a morphism whose kernel and cokernel are annihilated by certain non-zero integers. In this paper, the authors exploit this notion of almost-isomorphism to develop a homological algebra ``up to bounded torsion''. In particular, they define almost-projective modules, almost-projective resolution, \dots, and they show that the Tor and Ext functors can be computed up to almost-isomorphisms using almost-projective resolutions.
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20J06
Mathematics Subject Classification ID: 18G05
Mathematics Subject Classification ID: 18G10
Mathematics Subject Classification ID: 18G15
Mathematics Subject Classification ID: 18G20
zbMATH DE Number: 6242103
zbMATH Keywords: group cohomology
zbMATH Keywords: cohomological dimension
zbMATH Keywords: projective resolutions
zbMATH Keywords: almost-isomorphisms
zbMATH Keywords: Tor functor
zbMATH Keywords: Ext functor
reviewed by: Saïd Zarati
MaRDI profile type: Publication
full work available at URL: s00013-013-0574-4
OpenAlex ID: W2024467229
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DOI: 10.1007/S00013-013-0574-4
description: scientific article; zbMATH DE number 6242103