In this paper, we introduce the concept of a wide tensor category which is a special class of a tensor category initiated by the inverse braid monoids recently investigated by Easdown and Lavers [The Inverse BraidMonoid,Adv. inMath. 186 (2004) 438–455]. The inverse braid monoids IBn is an inverse monoid which behaves as the symmetric inverse semigroup so that the braid group Bn can be regarded ...

We define the braid groups of a two-dimensional orbifold and introduce conventions for drawing braid pictures. We use these to realize the Artin groups associated to the spherical Coxeter diagrams An, Bn = Cn and Dn and the affine diagrams Ãn, B̃n, C̃n and D̃n as subgroups of the braid groups of various simple orbifolds. The cases Dn, B̃n, C̃n and D̃n are new. In each case the Artin group is a normal...

The purpose of this article is to describe connections between the loop space of the 2-sphere, Artin’s braid groups, a choice of simplicial group whose homotopy groups are given by modules called Lie(n), as well as work of Milnor [25], and Habegger-Lin [17, 22] on ”homotopy string links”. The current article exploits Lie algebras associated to Vassiliev invariants in work of T. Kohno [19, 20], ...

Just as classical knots and links can be represented by the closures of braids, so can virtual knots and links be represented by the closures of virtual braids [17]. Virtual braids have a group structure that can be described by generators and relations, generalizing the generators and relations of the classical braid group. This structure of virtual braids is worth study for its own sake. The ...

Just as classical knots and links can be represented by the closures of braids, so can virtual knots and links be represented by the closures of virtual braids [16]. Virtual braids have a group structure that can be described by generators and relations, generalizing the generators and relations of the classical braid group. This structure of virtual braids is worth study for its own sake. The ...

In this note we solve the twisted conjugacy problem for braid groups, i.e. we propose an algorithm which, given two braids u, v ∈ Bn and an automorphism φ ∈ Aut(Bn), decides whether v = (φ(x))−1ux for some x ∈ Bn. As a corollary, we deduce that each group of the form Bn o H, a semidirect product of the braid group Bn by a torsion-free hyperbolic group H, has solvable conjugacy problem.