Links of intervals and the Gassner representation
type: Item
instance of: scholarly article
title: Links of intervals and the Gassner representation
zbMATH Open document ID: 0759.57010
DOI: 10.1007/BF02566502
published in: Commentarii Mathematici Helvetici
publication date: 1993-01-16T00:00:00Z
full work available at URL: https://eudml.org/doc/140271
review text: Let \(F\) be the free group on \(n\) generators and \(G\) its algebraic closure (in the sense of \textit{J. P. Levine} [ibid. 64, 236-255 (1989; Zbl 0692.57009) and Invent. Math. 96, 571-592 (1989; Zbl 0692.57010)]). The Cohn localization and homological ideas are used to extend the free differential calculus to \(G\) and hence to define a representation of the group of automorphisms of \(G\) which induce the identity on the abelianization into \(GL(n,\Lambda_ S)\), where \(\Lambda_ S\) is the localization of the integral Laurent polynomial ring in \(n\) commuting variables with respect to the multiplicative system of elements with augmentation 1. This representation is then used to extend the Gassner representation of the pure braid group on \(n\) strings to the group of concordance classes of links of \(n\) intervals in the 3-disc.
reviewed by: Jonathan A. Hillman
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 93810
zbMATH Keywords: free group on \(n\) generators
zbMATH Keywords: Cohn localization
zbMATH Keywords: free differential calculus
zbMATH Keywords: group of automorphisms
zbMATH Keywords: Gassner representation of the pure braid group
zbMATH Keywords: group of concordance classes of links
author: J.-Y. Le Dimet
MaRDI profile type: Publication
OpenAlex ID: W2136823826
description: scientific article; zbMATH DE number 93810