Related papers: Braid groups and Artin groups

We introduce and study a family of groups $\mathbf{BB}_n$, called the blocked-braid groups, which are quotients of Artin's braid groups $\mathbf{B}_n$, and have the corresponding symmetric groups $\Sigma_n$ as quotients. They are defined by…

Let $d \geq 2$ and $n\geq 3$ be two natural numbers. Given any sequence $\kappa=(k_1,\dots,k_n) \in \mathbb{Z}^n$ such that $\gcd(k_1,\dots,k_n,d)=1$, we consider the family of Riemann surfaces obtained from the plane curves defined by…

Ihara initiated to study a certain Galois representation which may be seen as an arithmetic analogue of the Artin representation of a pure braid group. We pursue the analogies in Ihara theory further, following after some issues and their…

Towards the study of the representation theory of any dihedral Artin group B, we build rational morphisms from B to the group of invertible elements of the associated infinitesimal braids algebra. For this we build analogues of Drinfeld…

The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed…

In this paper we construct a gathering process by the means of which we obtain new normal forms in braid groups. The new normal forms generalise Artin-Markoff normal forms and possess an extremely natural geometric description. In the two…

In this article, we introduce the notion of representations of polyadic groups and we investigate the connection between these representations and those of retract groups and covering groups.

Garside groups are a natural lattice-theoretic generalisation of the braid groups and spherical type Artin--Tits groups. Here we show that the class of Garside groups is closed under some free products with cyclic amalgamated subgroups. We…

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…

The result of this paper is the determination of the cohomology of Artin groups of type A_n, B_n and \tilde{A}_{n} with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type…

Similar pictures appear in various branches of mathematics. Sometimes this similarity gives rise to deep theorems. Mentioning such a similarity between hexagonal tilings, cubes in 3-space, configurations of lines and braid groups, we prove…

The braid group $B_{n}$, endowed with Artin's presentation, admits two distinguished involutions. One is the anti-automorphism ${\rm{rev}}: B_{n} \to B_{n}$, $v \mapsto \bar{v}$, defined by reading braids in the reverse order (from right to…

We establish a braid monodromy representation of functions satisfying an algebraic equation containing three terms (trinomial equation). We follow global analytic continuation of the roots to a trinomial algebraic equation that are…

This is a systematic introduction for physicists to the theory of algebras and groups with braid statistics, as developed over the last three years by the author. There are braided lines, braided planes, braided matrices and braided groups…

We propose two definitions of configuration Lie groupoids and in both the cases we prove a Fadell-Neuwirth type fibration theorem for a class of Lie groupoids. We show that this is the best possible extension, in the sense that, for the…

The $d$-fold ($d \geq 3$) branched coverings on a disk give an infinite family of nongeometric embeddings of braid groups into mapping class groups. We, in this paper, give new explicit expressions of these braid group representations into…

The topological model for quantum computation is an inherently fault-tolerant model built on anyons in topological phases of matter. A key role is played by the braid group, and in this survey we focus on a selection of ways that the…

The braid groups B_n can be defined as the mapping class group of the n-punctured disc. The Lawrence-Krammer representation of the braid group B_n is the induced action on a certain twisted second homology of the space of unordered pairs of…

Garside-theoretical solutions to the conjugacy problem in braid groups depend on the determination of a characteristic subset of the conjugacy class of any given braid, e.g. the sliding circuit set. It is conjectured that, among rigid…

Inverse braid monoid describes a structure on braids where the number of strings is not fixed. So, some strings of initial $n$ may be deleted. In the paper we show that many properties and objects based on braid groups may be extended to…