-knots via the mapping class group of the twice punctured torus.
A Garside presentation for Artin-Tits groups of type
We prove that an Artin-Tits group of type is the group of fractions of a Garside monoid, analogous to the known dual monoids associated with Artin-Tits groups of spherical type and obtained by the “generated group” method. This answers, in this particular case, a general question on Artin-Tits groups, gives a new presentation of an Artin-Tits group of type , and has consequences for the word problem, the computation of some centralizers or the triviality of the center. A key point of the proof...
A Jones polynomial for braid-like isotopies of oriented links and its categorification.
A Lagrangian representation of tangles II
The present paper is a continuation of our previous paper [Topology 44 (2005), 747-767], where we extended the Burau representation to oriented tangles. We now study further properties of this construction.
A note on the Lawrence-Krammer-Bigelow representation.
About presentations of braid groups and their generalizations
In the paper we give a survey of rather new notions and results which generalize classical ones in the theory of braids. Among such notions are various inverse monoids of partial braids. We also observe presentations different from standard Artin presentation for generalizations of braids. Namely, we consider presentations with small number of generators, Sergiescu graph-presentations and Birman-Ko-Lee presentation. The work of V.~V.~Chaynikov on the word and conjugacy problems for the singular...
Affine braid group actions on derived categories of Springer resolutions
In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a “categorical version” of Kazhdan-Lusztig-Ginzburg’s construction of the affine Hecke algebra, and is used in particular by the first author and I. Mirković in the course...
An acyclic extension of the braid group.
An approach to automorphisms of free groups and braids via transvections.
Anelli di coomologia dei gruppi di Artin
Arithmetic properties of the cohomology of Artin groups
Artin Groups and Infinite Coxeter Groups.
Automorphisms and abstract commensurators of 2-dimensional Artin groups.
Basic results on braid groups
These are Lecture Notes of a course given by the author at the French-Spanish School Tresses in Pau, held in Pau (France) in October 2009. It is basically an introduction to distinct approaches and techniques that can be used to show results in braid groups. Using these techniques we provide several proofs of well known results in braid groups, namely the correctness of Artin’s presentation, that the braid group is torsion free, or that its center is generated by the full twist. We also recall some...
Braid group action, embedding problems and the groups PGLn(q), Pun(q2).
Braided surfaces and Seifert ribbons for closed braids.
Braiding of the attractor and the failure of iterative algorithms.
Braids and invariants of 3-manifolds.
Braids: generalizations, presentations and algorithmic properties.
Braids in Pau – An Introduction
In this work, we describe the historic links between the study of -dimensional manifolds (specially knot theory) and the study of the topology of complex plane curves with a particular attention to the role of braid groups and Alexander-like invariants (torsions, different instances of Alexander polynomials). We finish with detailed computations in an example.