Algebraic & Geometric Topology

Random walk invariants of string links from R–matrices

Thomas Kerler and Yilong Wang

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Abstract

We show that the exterior powers of the matrix valued random walk invariant of string links, introduced by Lin, Tian, and Wang, are isomorphic to the graded components of the tangle functor associated to the Alexander polynomial by Ohtsuki divided by the zero graded invariant of the functor. Several resulting properties of these representations of the string link monoids are discussed.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 1 (2016), 569-596.

Dates
Received: 23 February 2015
Revised: 22 May 2015
Accepted: 4 June 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841120

Digital Object Identifier
doi:10.2140/agt.2016.16.569

Mathematical Reviews number (MathSciNet)
MR3470710

Zentralblatt MATH identifier
1346.57018

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 20F36: Braid groups; Artin groups 57R56: Topological quantum field theories 15A75: Exterior algebra, Grassmann algebras 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]

Keywords
string links tangles R-matrices Burau representation Alexander polynomial random walk

Citation

Kerler, Thomas; Wang, Yilong. Random walk invariants of string links from R–matrices. Algebr. Geom. Topol. 16 (2016), no. 1, 569--596. doi:10.2140/agt.2016.16.569. https://projecteuclid.org/euclid.agt/1510841120


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