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Fast Nielsen–Thurston classification of braids

Matthieu Calvez
Algebraic & Geometric Topology 14 (2014) 1745–1758
DOI: 10.2140/agt.2014.14.1745
Abstract

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.

Keywords
braid groups, Nielsen–Thurston classification
Mathematical Subject Classification 2010
Primary: 20F36
Secondary: 20F10, 20F65
References
Publication
Received: 26 January 2013
Revised: 7 October 2013
Accepted: 9 October 2013
Published: 29 May 2014
Authors
Matthieu Calvez
Departamento de Matemática y Ciencia de la Computación
Universidad de Santiago de Chile
Avenida Libertador Bernardo O’Higgins 3363
Estación Central
9160000 Santiago
Chile