Geodesic
The nth root of a braid is unique up to conjugacy
Gonzalez-Meneses, Juan1
1Universidad de Sevilla, Dep. Matemática Aplicada I, ETS Arquitectura, Av. Reina Mercedes 2, 41012-Sevilla, Spain
Algebraic and Geometric Topology, Tome 3 (2003) no. 2, pp. 1103-1118
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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.

DOI : 10.2140/agt.2003.3.1103
Keywords: braid, root, conjugacy, Nielsen-Thurston theory.

Gonzalez-Meneses, Juan  1

1 Universidad de Sevilla, Dep. Matemática Aplicada I, ETS Arquitectura, Av. Reina Mercedes 2, 41012-Sevilla, Spain 
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Gonzalez-Meneses, Juan. The nth root of a braid is unique up to conjugacy. Algebraic and Geometric Topology, Tome 3 (2003) no. 2, pp. 1103-1118. doi: 10.2140/agt.2003.3.1103

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