Random walk invariants of string links from R-matrices
type: Item
instance of: scholarly article
title: Random walk invariants of string links from R-matrices
zbMATH Open document ID: 1346.57018
author: Thomas Kerler
author: Yilong Wang
published in: Algebraic \& Geometric Topology
publication date: 2016-03-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/1406.2722
review text: A \textit{string link} is a tangle class \(T:\tau^n\rightarrow \tau^n\) with precisely \(n\) interval components, and a diagram where each interval has one endpoint at the bottom and the other endpoint at the top of the diagram. The authors show that the exterior powers of the matrix valued random walk invariant of string links, introduced by \textit{X.-S. Lin} et al. [Pac. J. Math. 182, No. 2, 289--302 (1998; Zbl 0903.57003)], are isomorphic to the graded components of the tangle functor associated to the Alexander polynomial by \textit{T. Ohtsuki} [Quantum invariants. A study of knots, 3-manifolds, and their sets. Singapore: World Scientific (2002; Zbl 0991.57001)] divided by the zero graded invariant of the functor. Several resulting properties of these representations of the string link monoids are discussed.
reviewed by: Claus Ernst
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 20F36
Mathematics Subject Classification ID: 57R56
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 6553368
zbMATH Keywords: string links
zbMATH Keywords: tangles
zbMATH Keywords: R-matrices
zbMATH Keywords: Burau representation
zbMATH Keywords: Alexander polynomial
zbMATH Keywords: random walk
MaRDI profile type: Publication
OpenAlex ID: W1591260833
arXiv ID: 1406.2722
DOI: 10.2140/AGT.2016.16.569
description: scientific article; zbMATH DE number 6553368