FAST ALGORITHMIC NIELSEN–THURSTON CLASSIFICATION OF FOUR-STRAND BRAIDS

DOI10.1142/S0218216511009959zbMath1251.20037arXiv1004.0067MaRDI QIDQ3225659

Matthieu Calvez, Bert Wiest

Publication date: 22 March 2012

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1004.0067

zbMATH Keywords

algorithmsNielsen-Thurston classificationreducible braids

Mathematics Subject Classification ID

Geometric group theory (20F65) Braid groups; Artin groups (20F36) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (5)

Reducible braids and Garside theory. ⋮ Fast Nielsen-Thurston classification of braids. ⋮ Dual Garside structure and reducibility of braids. ⋮ Efficient algorithm for recognizing the Nielsen-Thurston type of a three-strand braid. ⋮ On dilatation factors of braids on three strands

Cites Work

• Basic results on braid groups.
• Reducible braids and Garside theory.
• Abelian and solvable subgroups of the mapping class group
• A Garside-theoretic approach to the reducibility problem in braid groups.
• The cyclic sliding operation in Garside groups.
• Train-tracks for surface homeomorphisms
• Conjugacy problem for braid groups and Garside groups.
• Braid ordering and the geometry of closed braid
• Conjugacy in Garside groups. III: Periodic braids.
• A new approach to the conjugacy problem in Garside groups.
• ALGORITHMS FOR POSITIVE BRAIDS
• BRAIDS AND THE NIELSEN-THURSTON CLASSIFICATION
• THE BRAID GROUP AND OTHER GROUPS
• The infimum, supremum, and geodesic length of a braid conjugacy class.

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