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

Juan Gonzalez-Meneses

Algebraic & Geometric Topology 3 (2003) 1103–1118

arXiv: math.GT/0306070

Abstract

We prove a conjecture due to Makanin: if α and β are elements of the Artin braid group Bn such that αk = βk for some nonzero integer k, then α and β are conjugate. The proof involves the Nielsen–Thurston classification of braids.

Keywords
braid, root, conjugacy, Nielsen-Thurston theory.
Mathematical Subject Classification 2000
Primary: 20F36
Secondary: 20F65.
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Publication
Received: 29 June 2003
Revised: 16 October 2003
Accepted: 20 October 2003
Published: 1 November 2003
Authors
Juan Gonzalez-Meneses
Universidad de Sevilla
Dep. Matemática Aplicada I
ETS Arquitectura
Av. Reina Mercedes 2
41012-Sevilla
Spain
www.personal.us.es/meneses