منابع مشابه
Explicit Presentations for the Dual Braid Monoids
Birman, Ko & Lee have introduced a new monoid Bn—with an explicit presentation— whose group of fractions is the n-strand braid group Bn. Building on a new approach by Digne, Michel and himself, Bessis has defined a 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 a...
متن کاملThe Well-ordering of Dual Braid Monoids
We describe the restriction of the Dehornoy ordering of braids to the dual braid monoids introduced by Birman, Ko and Lee: we give an inductive characterization of the ordering of the dual braid monoids and compute the corresponding ordinal type. The proof consists in introducing a new ordering on the dual braid monoid using the rotating normal form of arXiv:math.GR/0811.3902, and then proving ...
متن کاملThe proof of Birman’s conjecture on singular braid monoids
Let Bn be the Artin braid group on n strings with standard generators σ1, . . . , σn−1 , and let SBn be the singular braid monoid with generators σ ±1 1 , . . . , σ ±1 n−1, τ1, . . . , τn−1 . The desingularization map is the multiplicative homomorphism η : SBn → Z[Bn] defined by η(σ ±1 i ) = σ ±1 i and η(τi) = σi − σ −1 i , for 1 ≤ i ≤ n − 1. The purpose of the present paper is to prove Birman’...
متن کاملFinite Thurston Type Orderings on Dual Braid Monoids
We give a combinatorial description of a finite Thurston type ordering < on the dual braid monoid B n by introducing the C-normal form and prove that the order-type of the well-ordered set (B n , <) is ωω n−2 . The C-normal form can be seen as a generalization of the rotating normal form defined by Fromentin and it is also a natural extension of C-normal form of the positive braid monoids defin...
متن کاملPartialization of Categories and Inverse Braid-Permutation Monoids
We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently defined inverse monoids, and use it to define a new object, which we call the inverse braid-permutation monoid. A presentation for this monoid is obtained. Fina...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2020
ISSN: 0166-8641
DOI: 10.1016/j.topol.2020.107118