On finite Thurston-type orderings of braid groups

DOI10.1515/GCC.2010.009zbMath1241.20040arXiv0810.4074MaRDI QIDQ3085990

Tetsuya Ito

Publication date: 1 April 2011

Published in: Groups – Complexity – Cryptology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.4074

zbMATH Keywords

braid groupsnormal form theoremsordinalsGarside monoidsbraid monoidsArtin-Tits groupsThurston-type orderings

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Braid groups; Artin groups (20F36) Ordered groups (06F15) Ordered groups (group-theoretic aspects) (20F60)

Related Items (3)

Every braid admits a short sigma-definite expression. ⋮ Laver's results and low-dimensional topology ⋮ A kernel of a braid group representation yields a knot with trivial knot polynomials

Cites Work

• A well-ordering of dual braid monoids.
• A new approach to the word and conjugacy problems in the braid groups
• The wellordering on positive braids
• Ordering the braid groups
• Computation of the ordinal of braids
• Order automatic mapping class groups
• Elementary Embeddings and Algebra
• THE WELL-ORDERING OF DUAL BRAID MONOID
• Braid Groups and Left Distributive Operations
• The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group
• Mapping class groups are automatic

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