Differential graded modules over a nonconnected differential graded algebra
type: Item
instance of: scholarly article
title: Differential graded modules over a nonconnected differential graded algebra
zbMATH Open document ID: 0729.55014
DOI: 10.1016/0022-4049(91)90129-P
author: N. E. Zubov
published in: Journal of Pure and Applied Algebra
publication date: 1991-01-01T00:00:00Z
review text: Let \(\Lambda_*\) be an associative differential graded algebras over a hereditary ring k. To each differential graded \(\Lambda_*\)-module \(M_*\) the author associates ``characteristic'' classes \(\theta_ q(M_*)\in Ext^ 2_{\Lambda}(H_ q(M_*),H_{q+1}(M_*))\) which depend only on the quasi-isomorphism class of \(M_*.\) If \(C_*\) is a dg-coalgebra and if t: \(C_*\to \Lambda_*\) is a twisting cochain, then there is a spectral sequence with \(E^ 2=H_ p(C_*;H_ q(M_*))\) converging to \(H_*(C_*\otimes_ tM_*)\). The author proves a formula (generalizing a formula of Hurewicz-Fadell) which expresses the \(d^ 2\)-differential in terms of the characteristic classes \(\theta_ q(M_*)\) and a class \([t^ 2]\in H^ 2(C_*;H_ 1(\Lambda_*))\) which is related to t. In particular, the author gives a formula (involving Stiefel-Whitney- classes) of the \(d^ 2\)-differential of the Serre spectral sequence of an O(n)-bundle \(X\to E\to B\).
Mathematics Subject Classification ID: 55T10
zbMATH DE Number: 4205404
zbMATH Keywords: differential graded algebras
zbMATH Keywords: twisting cochain
zbMATH Keywords: characteristic classes
zbMATH Keywords: Stiefel-Whitney-classes
zbMATH Keywords: Serre spectral sequence
zbMATH Keywords: O(n)-bundle
MaRDI profile type: Publication
cites work: Twisted tensor products. I
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cites work: Q3942064
cites work: Homotopie des espaces de sections
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full work available at URL: 0022-4049(91)90129-p
OpenAlex ID: W2088548098
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description: scientific article; zbMATH DE number 4205404