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2003 The $n$th root of a braid is unique up to conjugacy
Juan Gonzalez-Meneses
Algebr. Geom. Topol. 3(2): 1103-1118 (2003). DOI: 10.2140/agt.2003.3.1103

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.

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Juan Gonzalez-Meneses. "The $n$th root of a braid is unique up to conjugacy." Algebr. Geom. Topol. 3 (2) 1103 - 1118, 2003. https://doi.org/10.2140/agt.2003.3.1103

Information

Received: 29 June 2003; Revised: 16 October 2003; Accepted: 20 October 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1063.20041
MathSciNet: MR2012967
Digital Object Identifier: 10.2140/agt.2003.3.1103

Subjects:
Primary: 20F36
Secondary: 20F65.

Keywords: Braid , conjugacy , Nielsen-Thurston theory. , root

Rights: Copyright © 2003 Mathematical Sciences Publishers

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