The $n$th root of a braid is unique up to conjugacy.

Gonzalez-Meneses, Juan. "The th root of a braid is unique up to conjugacy.." Algebraic & Geometric Topology 3 (2003): 1103-1118. <http://eudml.org/doc/124658>.

@article{Gonzalez2003,
author = {Gonzalez-Meneses, Juan},
journal = {Algebraic & Geometric Topology},
keywords = {braid groups; unique roots; conjugacy; Nielsen-Thurston theory},
language = {eng},
pages = {1103-1118},
publisher = {Geometry & Topology Publications, Mathematics Institute, University of Warwick, Coventry; Mathematical Sciences Publishers, Berkeley},
title = {The th root of a braid is unique up to conjugacy.},
url = {http://eudml.org/doc/124658},
volume = {3},
year = {2003},
}

TY - JOUR
AU - Gonzalez-Meneses, Juan
TI - The th root of a braid is unique up to conjugacy.
JO - Algebraic & Geometric Topology
PY - 2003
PB - Geometry & Topology Publications, Mathematics Institute, University of Warwick, Coventry; Mathematical Sciences Publishers, Berkeley
VL - 3
SP - 1103
EP - 1118
LA - eng
KW - braid groups; unique roots; conjugacy; Nielsen-Thurston theory
UR - http://eudml.org/doc/124658
ER -