\(\Gamma\)-homology, topological André-Quillen homology and stabilization
type: Item
instance of: scholarly article
title: \(\Gamma\)-homology, topological André-Quillen homology and stabilization
zbMATH Open document ID: 1004.55003
DOI: 10.1016/S0166-8641(01)00098-0
author: Maria Basterra
author: Randy McCarthy
published in: Topology and its Applications
publication date: 2002-08-22T00:00:00Z
review text: The authors describe and compare three different homology constructions related to \(E_\infty\)-algebras: the \(\Gamma\)-homology, \(H_*^\Gamma\), of Robinson and Whitehouse, the topological André-Quillen homology, \(H_*^Q\), and the stabilization. They prove that the constructions agree when specialized to commutative rings. In particular, let \(k\) be a commutative ring, \(A\) be a commutative \(k\)-algebra, and \(Hk\) and \(HA\) be the corresponding Eilenberg-MacLane cofibrant commutative simplicial algebras, then there is an isomorphism of graded groups \(H_*^\Gamma(A/k;A)= H_*^Q (HA/Hk;HA)\).
Mathematics Subject Classification ID: 55P43
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 55N35
zbMATH DE Number: 1787544
zbMATH Keywords: \(E_\infty\) homology
reviewed by: Yves Félix
MaRDI profile type: Publication
cites work: Méthode simpliciale en algèbre homologique et algèbre commutative
cites work: André-Quillen cohomology of commutative \(S\)-algebras
cites work: Q4867806
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cites work: Robinson-Whitehouse complex and stable homotopy
cites work: Homotopical algebra
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description: scientific article; zbMATH DE number 1787544