The n-th root of a braid is unique up to conjugacy

Abstract

We prove a conjecture due to Makanin: if a and b are elements of the Artin braid group B_n such that a^k=b^k for some nonzero integer k, then a and b are conjugate. The proof involves the Nielsen-Thurston classification of braids.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-39.abs.html

References in corpus (1)

• The theorem of Kerekjarto on periodic homeomorphisms of the disc and the sphere

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