Related papers: Finiteness of algebraic fundamental groups

In this article we prove results about finite soluble groups that act with fixity 2 or 3.

In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…

The principle result of this article is the determination of the possible finite subgroups of arithmetic lattices in U(2,1).

Log-Riemann surfaces of finite type are Riemann surfaces with finitely generated fundamental group equipped with a local diffeomorphism to C such that the surface has finitely many infinite order ramification points. We define and prove…

We prove that for any e>0, there exists only finitely many e-log terminal spherical Fano varieties of fixed dimension. We also introduce an invariant of a spherical subgroup H in a reductive group G which measures how nice an equivariant…

The main result of this paper is the following theorem. Let q be a prime, A an elementary abelian group of order q^3. Suppose that A acts as a coprime group of automorphisms on a profinite group G in such a manner that C_G(a)' is periodic…

For any finitely presentable group $G$, we show the existence of an isolated complex surface singularity link which admits infinitely many exotic Stein fillings such that the fundamental group of each filling is isomorphic to $G$. We also…

Recently, Morier-Genoud and Ovsienko introduced the $q$-deformed modular group. For construction, they first gave a group $G_q \subset \operatorname{GL}(2, {\mathbb Z}[q^{\pm}])$ and then set $\operatorname{PSL}_q(2,{\mathbb…

This paper contributes to a theory of the behaviour of "finite-state" systems that is generic in the system type. We propose that such systems are modelled as coalgebras with a finitely generated carrier for an endofunctor on a locally…

We prove that a finite-dimensional omega-categorical group is finite-by-abelian-by-finite and that a finite-dimensional omega-categorical ring is virtually finite-by-null.

We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$, to be related by an ambient…

We prove a finiteness result for the systolic area of groups, answering a question of M. Gromov. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of~2-complexes whose systolic area is uniformly…

We show that every finite group occurs as the automorphism group of infinitely many finite (field) extensions of any given Hilbertian field. This extends and unifies previous results of M. Fried and Takahashi on the global field case.

We describe structure of locally finite groups of finite centraliser dimension.

We provide a complete classification of the singularities of cluster algebras of finite cluster type. This extends our previous work about the case of trivial coefficients. Additionally, we classify the singularities of cluster algebras for…

We study the topological fundamental groups of the locally finite infinite ordered configuration space \(Conf^{lf}_\infty(\C)\) in the plane and the homotopy quotient of $Conf^{lf}_\infty$ by the canonical action of the infinite permutation…

We show that a finite group $G$ admitting an automorphism $\alpha$ such that the function $G\rightarrow G$, $g\mapsto g\alpha(g)$, is bijective is necessarily solvable.

We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.

We prove that the local accumulation complexity of the set of log canonical volumes in dimension $\geq 2$ can be infinite.

This paper gives a quick overview of the author's recent result that all finitely presented groups are QSF.