The nth root of a braid is unique up to conjugacy

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 2000

Primary: 20F36

Secondary: 20F65.

References

Forward citations

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

Volume 3, issue 2 (2003)

Juan Gonzalez-Meneses