Related papers: Infinitesimal finiteness obstructions

We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…

We consider the following question, concerning associative algebras R over an algebraically closed field k: When can the space of (equivalence classes of) finite dimensional irreducible representations of R be topologically embedded into a…

We describe various classes of infinitely presented groups that are condensation points in the space of marked groups. A well-known class of such groups consists of finitely generated groups admitting an infinite minimal presentation. We…

In this article, we investigate the status of the homomorphism preservation property amongst restricted classes of finite relational structures and algebraic structures. We show that there are many homomorphism-closed classes of finite…

We prove that there are only finitely many closed hyperbolic 3-manifolds with injectivity radius and first eigenvalue of the Laplacian bounded below whose fundamental groups can be generated by a given number of elements. An application to…

Let X be a finite CW-complex of dimension q. If its fundamental group $\pi_{1}(X)$ is polycyclic of Hirsch number h>q we show that at least one of the homotopy groups $\pi_{i}(X)$ is not finitely generated. If h=q or h=q-1 the same…

Gromov asked what a typical (finitely presented) group looks like, and he suggested a way to make the question precise in terms of limiting density. The typical finitely generated group is known to share some important properties with the…

Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…

Homogenization is a powerful way of taming a class of finite structures with several interesting applications in different areas, from Ramsey theory in combinatorics to constraint satisfaction problems (CSPs) in computer science, through…

By operations on models we show how to relate completeness with respect to permissive-nominal models to completeness with respect to nominal models with finite support. Models with finite support are a special case of permissive-nominal…

We show that any closed biquotient with finite fundamental group admits metrics of positive Ricci curvature. Also, let M be a closed manifold on which a compact Lie group G acts with cohomogeneity one, and let L be a closed subgroup of G…

We consider linear groups which do not contain unipotent elements of infinite order, which includes all linear groups in positive characteristic, and show that this class of groups has good properties which resemble those held by groups of…

Given a closed smooth manifold $M$ of even dimension $2n\ge6$ with finite fundamental group, we show that the classifying space ${\rm BDiff}(M)$ of the diffeomorphism group of $M$ is of finite type and has finitely generated homotopy groups…

We prove that a finitely generated group contains a sequence of non-trivial elements which converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian.

The concept of a C-approximable group, for a class of finite groups C, is a common generalization of the concepts of a sofic, weakly sofic, and linear sofic group. Glebsky raised the question whether all groups are approximable by finite…

We study the automorphism group of the algebraic closure of a substructure A of a pseudo-finite field F, or more generally, of a bounded PAC field F. This paper answers some of the questions of [1], and in particular that any finite group…

Let $m\geq 3$ be a positive integer. We prove that there are uncountably many non-commensurable metabelian uniform pro-$p$ groups of dimension $m$. Consequently, there are uncountably many non-commensurable finitely presented pro-$p$ groups…

We prove the Haagerup property (= Gromov's a-T-menability) for finitely generated groups defined by infinite presentations satisfying the C'(1/6)-small cancellation condition. We deduce that these groups are coarsely embeddable into a…

We prove that Hausdorff limit of topological minimal sets (with finitely generated coefficient group) are topologically minimal. The key idea is to reduce the homology group on the space to the homology group on the sphere, and reduce the…

Let $G$ be a locally compact amenable group. We say that G has property (M) if every closed subgroup of finite covolume in G is cocompact. A classical theorem of Mostow ensures that connected solvable Lie groups have property (M). We prove…