Volume 16, issue 1 (2016)

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Random walk invariants of string links from R–matrices

Thomas Kerler and Yilong Wang

Algebraic & Geometric Topology 16 (2016) 569–596

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.

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string links, tangles, R-matrices, Burau representation, Alexander polynomial, random walk
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25, 20F36, 57R56, 15A75, 17B37
Received: 23 February 2015
Revised: 22 May 2015
Accepted: 4 June 2015
Published: 23 February 2016
Thomas Kerler
Department of Mathematics
Ohio State University
Columbus, OH 43210
Yilong Wang
Department of Mathematics
Ohio State University
Columbus, OH 43210