Explicit Presentations for the Dual Braid Monoids

Details Explicit Presentations for the Dual Braid Monoids Explicit Presentations for the Dual Braid Monoids

2001-11-27

arxiv.org/abs/math/0111280v1

Mathematics

Group Theory

6 pages, 4 figures

Scientific paper

Birman, Ko and Lee have introduced a new monoid ${\cal B}^{*}_{n}$--with an explicit presentation--whose group of fractions is the $n$-strand braid group ${\cal B}_{n}$. 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.

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