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A NONDEGENERATE EXCHANGE MOVE ALWAYS PRODUCES INFINITELY MANY NONCONJUGATE BRAIDS

  • TETSUYA ITO (a1)

Abstract

We show that if a link $L$ has a closed $n$ -braid representative admitting a nondegenerate exchange move, an exchange move that does not obviously preserve the conjugacy class, $L$ has infinitely many nonconjugate closed $n$ -braid representatives.

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[Sh]Shinjo, R., Non-conjugate braids whose closures result in the same knot, J. Knot Theory Ramifications 19 (2010), 117124.
[SS]Shinjo, R. and Stoimenow, A., Exchange moves and non-conjugate braid representatives of knots, Nagoya Math J. to appear, doi:10.1017/nmj.2019.10.
[St1]Stoimenow, A., On non-conjugate braids with the same closure link, J. Geom. 96 (2009), 179186.
[St2]Stoimenow, A., Non-conjugate braids with the same closure link from density of representations, J. Math. Pures Appl. 94(9) (2010), 470496.
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A NONDEGENERATE EXCHANGE MOVE ALWAYS PRODUCES INFINITELY MANY NONCONJUGATE BRAIDS

  • TETSUYA ITO (a1)

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