Exchange moves and braid representations of links

2011/03/13 by Reiko Shinjo, Shinjo, Reiko, A. Stoimenow +2
Mathematics · #Advanced Combinatorial Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:20F36 #msc:57M25 #msc:57M27

paper · pdf · doi:10.48550/arxiv.1103.2510

25 pages, 17 figures

arxiv created 2011/03/13 · arxiv updated 2011/03/15

Abstract

We prove that under fairly general conditions an iterated exchange move gives infinitely many non-conjugate braids. As a consequence, every knot has infinitely many conjugacy classes of n-braid representations if and only if it has one admitting an exchange move.

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