Lazard completion of a group and free differential graded algebra models over subrings of the rationals
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.
scientific article; zbMATH DE number 3917252