Related papers: Orbifold braid groups and complex braid groups

We study the action of the Artin braid group B_{2g+2} on the set of spin structures on a hyperelliptic curve of genus g, which reduces to that of the symmetric group. It has been already described in terms of the classical theory of Riemann…

We introduce the class of perturbed right-angled Artin groups. These are constructed by gluing Bieri double groups into standard right-angled Artin groups. As a first application of this construction we obtain families of CAT(0) groups…

We are interested in finite groups acting orientation-preservingly on 3-manifolds (arbitrary actions, ie not necessarily free actions). In particular we consider finite groups which contain an involution with nonempty connected fixed point…

We show that Artin groups of extra-large type, and more generally Artin groups of large and hyperbolic type, are hierarchically hyperbolic. This implies in particular that these groups have finite asymptotic dimension and uniform…

We describe a series of complexes that relate to the braid groups as the matching complexes relate to the symmetric groups. A modified construction applies as well to other complexes based on edge sets in graphs. We show that our…

In the first part we review some topological and algebraic aspects in the theory of Artin and Coxeter groups, both in the finite and infinite case (but still, finitely generated). In the following parts, among other things, we compute the…

For every $n\ge 2$, the {\em surface Houghton group} $\mathcal B_n$ is defined as the asymptotically rigid mapping class group of a surface with exactly $n$ ends, all of them non-planar. The groups $\mathcal B_n$ are analogous to, and in…

This is a draft of a book submitted for publication by the AMS. Its theme is the remarkable interplay, accelerating in the last few decades, between topology and the theory of orderable groups, with applications in both directions. It…

We show that any finitely presented group with an index two subgroup is realized as the fundamental group of a closed smooth non-orientable four-manifold that admits an exotic smooth structure, which is obtained by performing a Gluck twist.…

This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those with finitely many clusters. This classification turns out…

Let {T_n} be the bipolar filtration of the smooth concordance group of topologically slice knots, which was introduced by Cochran, Harvey, and Horn. It is known that for each n not equal to 1 the quotient group T_n/T_{n+1} has infinite rank…

We define the intersection complex for the universal cover of a compact weakly special square complex and show that it is a quasi-isometry invariant. By using this quasi-isometry invariant, we study the quasi-isometric classification of…

We compute the automorphism group of the intersection graph of many large-type Artin groups. This graph is an analogue of the curve graph of mapping class groups but in the context of Artin groups. As an application, we deduce a number of…

We prove that acylindrically hyperbolic groups are monotileable. That is, every finite subset of the group is contained in a finite tile. This provides many new examples of monotileable groups, and progress on the question of whether every…

The main result of this article is that pure orbifold braid groups fit into an exact sequence $1\rightarrow…

Let g and n be integers at least two, and let G be the pure braid group with n strands on a closed orientable surface of genus g. We describe any injective homomorphism from a finite index subgroup of G into G. As a consequence, we show…

We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the…

Artin's braid groups have been recently suggested as a new source for public-key cryptography. In this paper we propose the first group signature schemes based on the conjugacy problem, decomposition problem and root problem in the braid…

Gonz{\'a}lez-Acu{\~n}a showed that Artin presentations characterize closed, orientable $3$-manifold groups. Winkelnkemper later discovered that each Artin presentation determines a smooth, compact, simply-connected $4$-manifold. We utilize…

We define an action of Artin's braid group on a finite dimensional algebra.