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Fast algorithmic Nielsen-Thurston classification of four-strand braids

 

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Opened Access Fast algorithmic Nielsen-Thurston classification of four-strand braids
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Author: Calvez, Matthieu
Wiest, Bert
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2012-04
Published in: Journal of Knot Theory and Its Ramifications, 21 (5), 1250043-1-1250043-25.
Document type: Article
Abstract: We give an algorithm which decides the Nielsen-Thurston type of a given four-strand braid. The complexity of our algorithm is quadratic with respect to word length. The proof of its validity is based on a result which states that for a reducible 4-braid which is as short as possible within its conjugacy class (short in the sense of Garside), reducing curves surrounding three punctures must be round or almost round. As an application, we give a polynomial time solution to the conjugacy problem for non-pseudo-Anosov four-strand braids.
Cite: Calvez, M. y Wiest, B. (2012). Fast algorithmic Nielsen-Thurston classification of four-strand braids. Journal of Knot Theory and Its Ramifications, 21 (5), 1250043-1-1250043-25.
Size: 379.4Kb
Format: PDF

URI: http://hdl.handle.net/11441/47584

DOI: 10.1142/S0218216511009959

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