Related papers: Cycle groups for Artin stacks
We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.
We prove the Farrell-Jones fibered isomorphism conjecture for several classes of Artin groups of finite and affine types. As a consequence, we compute explicitly the surgery obstruction groups of the finite type pure Artin groups.
We consider the problem of deciding if a group is the fundamental group of a smooth connected complex quasi-projective (or projective) variety using Alexander-based invariants. In particular, we solve the problem for large families of…
We give a brief introduction to the geometric and combinatorial group theory of Artin groups. In particular we introduce the $K(\pi,1)$ conjecture for Artin groups and survey known results as of January 2024. These notes were written as…
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…
We prove that an Artin group splits over infinite cyclic subgroups if and only if its defining graph has a separating vertex, and explicitly construct a JSJ decomposition over infinite cyclic subgroups for all Artin groups. We then use…
In this note we show that an Artin stack with finite inertia stack is etale locally isomorphic to the quotient of an affine scheme by an action of a general linear group.
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 groups whose Dynkin diagrams contain a cycle, which…
We observe that, for each positive integer n > 2, each of the Artin groups of finite type A_n, B_n=C_n, and affine type \tilde A_{n-1} and \tilde C_{n-1} is a central extension of a finite index subgroup of the mapping class group of the…
We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of \'etale, smooth, or syntomic neighborhoods of closed subschemes and closed substacks. In particular, we prove…
We study the Artin Approximation property with constraints in a different frame. As a consequence we give a nested Artin Strong Approximation property for algebraic power series rings over a field.
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…
Let $\Gamma$ be a finite graph and let $A(\Gamma)$ be the corresponding right-angled Artin group. We characterize the Hamiltonicity of $\Gamma$ via the structure of the cohomology algebra of $A(\Gamma)$. In doing so, we define and develop a…
We give a proof of openness of versality using coherent functors. As an application, we streamline Artin's criterion for algebraicity of a stack. We also introduce multi-step obstruction theories, employing them to produce obstruction…
This is the first in a series of papers devoted to foundations of topological stacks. We begin developing a homotopy theory for topological stacks along the lines of classical homotopy theory of topological spaces. In this paper we go as…
We study fundamental groups of algebraic stacks. We show that these fundamental groups carry an additional structure coming from the inertia groups. Then use this additional structure to analyze geometric/ topological properties of stacks.…
This paper analyzes the second cohomology group of a linear cycle set with coefficients in an abelian group I, for linear cycle sets with commutative adjoint operation, focusing on the finite abelian case. It aims to classify extensions of…
We introduce a new cohomology theory for stacks called elliptic Hochschild homology, prove some fundamental properties and compute it in some classes of examples. We then introduce its periodic cyclic version and show that, over the complex…
We give a complete characterisation of when the right-angled Artin group on one cycle graph can be quasiisometrically embedded in the right-angled Artin group on another cycle graph. In particular, we find infinitely many instances of…
Given a finite graph G there is a corresponding group given by the presentation with generators the vertices of G and a relation [x,y]=1 for generators x and y precisely when (x,y) is an edge of G. Such groups are known as partially…