Lazard completion of a group and free differential graded algebra models over subrings of the rationals
type: Item
instance of: scholarly article
title: Lazard completion of a group and free differential graded algebra models over subrings of the rationals
zbMATH Open document ID: 0574.55006
DOI: 10.1016/0040-9383(84)90005-3
author: B. George
published in: Topology
publication date: 1984-01-01T00:00:00Z
review text: The paper continues a previous investigation by the authors [Adv. Math. 48, 189-204 (1983; Zbl 0526.55013)]. Let X be a connected simplicial set with \(H_ 1(X;{\mathbb{Z}})\) finitely generated. The algebra of tame (cubical) forms on X then has a 1-minimal model which gives rise to a Lazard Lie algebra L(X). By the Lazard correspondence L(X) is also a group with the group structure defined by the Baker-Campbell-Hausdorff formula. A (natural) homomorphism from \(\pi_ 1(X)\) into the group L(X) is contructed which induces an isomorphism between the Lazard completion of \(\pi_ 1(X)\) and the group L(X). This intricate construction is based on the technique of iterated integrals (adapted to the tame situation) and on results of K. T. Chen.
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 55P60
Mathematics Subject Classification ID: 20F14
zbMATH DE Number: 3917252
zbMATH Keywords: algebra of tame forms
zbMATH Keywords: 1-minimal model
zbMATH Keywords: Lazard Lie algebra
zbMATH Keywords: Lazard correspondence
zbMATH Keywords: Baker-Campbell-Hausdorff formula
zbMATH Keywords: Lazard completion
zbMATH Keywords: iterated integrals
reviewed by: Hans Scheerer
MaRDI profile type: Publication
full work available at URL: 0040-9383(84)90005-3
OpenAlex ID: W1989516675
description: scientific article; zbMATH DE number 3917252