On finite Thurston type orderings of braid groups

Abstract

We prove that for any finite Thurston-type ordering ${<}_T$ on the braid group\ $B_n$, the restriction to the positive braid monoid $(B_n^{+},{<}_T)$ is a\ well-ordered set of order type ${\omega }^{{\omega }^{n-2}}$. The proof uses a combi\ natorial description of the ordering ${<}_T$. Our combinatorial description is \ based on a new normal form for positive braids which we call the $\C$-normal fo\ rm. It can be seen as a generalization of Burckel's normal form and Dehornoy's \ $\Phi$-normal form (alternating normal form).

25 pages, 2 figures; proof of Theorem 1 is corrected

References in corpus (3)

• The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group
• Every braid admits a short sigma-definite representative
• Braid ordering and knot genus

Cited by in corpus (2)

• Unprovability results involving braids
• Every braid admits a short sigma-definite representative