Algebraic and Geometric Topology 3 (2003), paper no. 39, pages 1103-1118.

The nth root of a braid is unique up to conjugacy

Juan Gonzalez-Meneses

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

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

AMS subject classification. Primary: 20F36. Secondary: 20F65..

DOI: 10.2140/agt.2003.3.1103

E-print: arXiv:math.GT/0306070

Submitted: 29 June 2003. (Revised: 16 October 2003.) Accepted: 20 October 2003. Published: 1 November 2003.

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Juan Gonzalez-Meneses
Universidad de Sevilla. Dep. Matematica Aplicada I
ETS Arquitectura, Av. Reina Mercedes 2, 41012-Sevilla, Spain
Email: meneses@us.es
URL: http://www.personal.us.es/meneses
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