Algebraic & Geometric Topology 3 (2003) 1103–1118

DOI: 10.2140/agt.2003.3.1103

arXiv: math.GT/0306070

Abstract

We prove a conjecture due to Makanin: if α and β are elements of the Artin braid group B_n such that α^k = β^k 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

Primary: 20F36

Secondary: 20F65.

References

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Publication

Received: 29 June 2003
Revised: 16 October 2003
Accepted: 20 October 2003
Published: 1 November 2003

Authors