Hyperplane arrangement theory is a very active area of research, combining ideas from
combinatorics, algebraic topology and algebraic geometry in a blend that is both tasty and …

We prove the K (π, 1) K (π, 1) conjecture for affine Artin groups: the complexified
complement of an affine reflection arrangement is a classifying space. This is a long …

This paper is a short survey on four basic questions on Artin-Tits groups: the torsion, the
center, the word problem, and the cohomology (K (π, 1) problem). It is also an opportunity to …

We show that for a large class of Artin groups with Dynkin diagrams being a tree, the\(K (\pi,
1)\)-conjecture holds. We also establish the\(K (\pi, 1)\)-conjecture for another class of Artin …

Artin groups are easily defined but most of them are poorly understood. In this survey I try to
highlight precisely where the problems begin. The first part reviews the close connection …

A certain structure of Artin groups and the isomorphism conjecture Page 1 Canad. J. Math. Vol.
( ), pp. – http://dx.doi.org/ . /SXX © Canadian Mathematical Society A certain structure of Artin …

We extend the theory of dual Coxeter and Artin groups to all rank-three Coxeter systems,
beyond the previously studied spherical and affine cases. Using geometric, combinatorial …

This article is a survey on the braid groups, the Artin groups, and the Garside groups. It is a
presentation, accessible to non-experts, of various topological and algebraic aspects of …

We expand the theory of weighted sheaves over posets, and use it to study the local
homology of Artin groups. First, we use such theory to relate the homology of classical braid …

Artin groups span a wide range of groups from braid groups to free groups to free abelian
groups, as well as many more exotic groups. In recent years, Artin groups and their …