FINITE THURSTON-TYPE ORDERINGS ON DUAL BRAID MONOIDS

Abstract

For a finite Thurston-type ordering < of the braid group Bn, we introduce a new normal form of a dual positive braid which we call the [Formula: see text]-normal form, which is useful to compute the ordering. This normal form extends Fromentin's rotating normal form and the author's [Formula: see text]-normal form of positive braids. Using the [Formula: see text]-normal form, we give a combinatorial description of the restriction of the ordering < to the dual braid monoids [Formula: see text]. We prove that the restriction to the dual positive monoid [Formula: see text] is a well-ordered set of the order type ωωn-2.