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EXCHANGE MOVES AND NONCONJUGATE BRAID REPRESENTATIVES OF KNOTS

Part of: Low-dimensional topology Special aspects of infinite or finite groups

Published online by Cambridge University Press:  20 May 2019

REIKO SHINJO  and
ALEXANDER STOIMENOW
REIKO SHINJO
Affiliation:
School of Science and Engineering, Kokushikan University, 4-28-1 Setagaya, Setagaya-ku, Tokyo 154-8515, Japan email reiko@kokushikan.ac.jp
ALEXANDER STOIMENOW
Affiliation:
School of General Studies, Gwangju Institute of Science and Technology, Gwangju 61005, Korea email stoimeno@stoimenov.nethttp://stoimenov.net/stoimeno/homepage/
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Abstract

We prove that for $n\geqslant 4$, every knot has infinitely many conjugacy classes of $n$-braid representatives if and only if it has one admitting an exchange move.

MSC classification

Primary: 57M25: Knots and links in $S^3$
Secondary: 20F36: Braid groups; Artin groups 57M27: Invariants of knots and 3-manifolds
Type
Article
Information
Nagoya Mathematical Journal , Volume 240 , December 2020 , pp. 298 - 321
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Copyright
© 2019 Foundation Nagoya Mathematical Journal

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