Related papers: Quasi-projectivity, Artin-Tits Groups, and Pencil …
We show that quasi-projective Bestvina-Brady groups are fundamental groups of complements to hyperplane arrangements. Furthermore we relate other normal subgroups of right-angled Artin groups to complements to arrangements of hypersurfaces.…
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 show that the fundamental groups of any two closed irreducible non-geometric graph-manifolds are quasi-isometric. This answers a question of Kapovich and Leeb. We also classify the quasi-isometry types of fundamental groups of…
Even Artin groups generalize right-angled Artin groups by allowing the labels in the defining graph to be even. In this paper a complete characterization of quasi-projective even Artin groups is given in terms of their defining graphs.…
We describe the structure of quasiflats in two-dimensio\-nal Artin groups. We rely on the notion of metric systolicity developed in our previous work. Using this weak form of non-positive curvature and analyzing in details the combinatorics…
We survey various Alexander-type invariants of plane curve complements, with an emphasis on obstructions on the type of groups that can arise as fundamental groups of complements to complex plane curves. Also included are some new…
We study the geometry of nonrelatively hyperbolic groups. Generalizing a result of Schwartz, any quasi-isometric image of a non-relatively hyperbolic space in a relatively hyperbolic space is contained in a bounded neighborhood of a single…
We present two results about the relationship between fundamental groups of quasiprojective manifolds and linear systems on a projectivization. We prove the existence of a plane curve with non-abelian fundamental group of the complement…
Artin groups of finite type are not as well understood as braid groups. This is due to the additional geometric properties of braid groups coming from their close connection to mapping class groups. For each Artin group of finite type, we…
In \cite{Oh22}, the second author defined a complex of groups decomposition of the fundamental group of a finitely generated 2-dimensional special group, called an \emph{intersection complex}, which is a quasi-isometry invariant. In this…
The present paper describes a relation between the quotient of the fundamental group of a smooth quasi-projective variety by its second commutator and the existence of maps to orbifold curves. It extends previously studied cases when the…
We prove several results on the model theory of Artin groups, focusing on Artin groups which are ``far from right-angled Artin groups''. The first result is that if $\mathcal{C}$ is a class of Artin groups whose irreducible components are…
The paper reviews recent developments in the study of Alexander invariants of quasi-projective manifolds using methods of singularity theory. Several results in topology of the complements to singular plane curves and hypersurfaces in…
For a one-ended right-angled Artin group, we give an explicit description of its JSJ tree of cylinders over infinite cyclic subgroups in terms of its defining graph. This is then used to classify certain right-angled Artin groups up to…
A finite simple graph \G determines a right-angled Artin group G_\G, with one generator for each vertex v, and with one commutator relation vw=wv for each pair of vertices joined by an edge. The Bestvina-Brady group N_\G is the kernel of…
We define for every affine Coxeter graph a certain factor group of the associated Artin group and prove that some of these groups appear as orbifold fundamental groups of moduli spaces. Examples are the moduli space of nonsingular cubic…
We survey the cohomology jumping loci and the Alexander-type invariants associated to a space, or to its fundamental group. Though most of the material is expository, we provide new examples and applications, which in turn raise several…
In this summary paper, we present the key ideas behind the recent proof of the $K(\pi, 1)$ conjecture for affine Artin groups, which states that complements of locally finite affine hyperplane arrangements with real equations and stable…
We consider the structure of classes of curves on a projective simply connected surface for which fundamental groups of the complements admit free quotients having rank greater than one with irreducible components belonging to a selected…
We explore the codimension one strata in the degree-one cohomology jumping loci of a finitely generated group, through the prism of the multivariable Alexander polynomial. As an application, we give new criteria that must be satisfied by…