Algebraic & Geometric Topology

Fast Nielsen–Thurston classification of braids

Matthieu Calvez

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We prove the existence of an algorithm that solves the reducibility problem in braid groups and runs in quadratic time with respect to the braid length for any fixed braid index.

Article information

Algebr. Geom. Topol., Volume 14, Number 3 (2014), 1745-1758.

Received: 26 January 2013
Revised: 7 October 2013
Accepted: 9 October 2013
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F36: Braid groups; Artin groups
Secondary: 20F10: Word problems, other decision problems, connections with logic and automata [See also 03B25, 03D05, 03D40, 06B25, 08A50, 20M05, 68Q70] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]

braid groups Nielsen–Thurston classification


Calvez, Matthieu. Fast Nielsen–Thurston classification of braids. Algebr. Geom. Topol. 14 (2014), no. 3, 1745--1758. doi:10.2140/agt.2014.14.1745.

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