Explicit Presentations for the Dual Braid Monoids

Abstract

Birman, Ko and Lee have introduced a new monoid ${\mathcal{B}}_n^{\ast }$--with an explicit presentation--whose group of fractions is the $n$-strand braid group ${\mathcal{B}}_n$. Building on a new approach by Digne, Michel and himself, Bessis has defined a {\it dual} braid monoid for every finite Coxeter type Artin-Tits group extending the type A case. Here, we give an explicit presentation for this dual braid monoid in the case of types B and D, and we study the combinatorics of the underlying Garside structures.

6 pages, 4 figures