Finite Thurston type orderings on dual braid monoids

Details Finite Thurston type orderings on dual braid monoids Finite Thurston type orderings on dual braid monoids

2009-02-05

arxiv.org/abs/0902.0833v2

J. Knot Theory Ramifications 20 (2011), 995-1019

Mathematics

Group Theory

28pages, 5 figures

Scientific paper

10.1142/S0218216511009078

For a finite Thurston type ordering < of the braid group B_{n}, we introduce a new normal form of a dual positive braid which we call the C-normal form. This normal form extends Fromentin's rotating normal form and the author's C-normal form of positive braids. Using the C-normal form, we give a combinatorial description of the restriction of the ordering < to the dual braid monoids B_{n}^{+*}. We prove that the restriction to the dual positive monoid (B_{n}^{+*},<) is a well-ordered set of order type \omega^{\omega^{n-2}}.

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