Related papers: On the genus of infinite groups

We study compact K\"ahler threefolds X with infinite fundamental group whose universal cover can be compactified. Combining techniques from $L^2$ -theory, Campana's geometric orbifolds and the minimal model program we show that this…

We construct new examples of immersed minimal surfaces with catenoid ends and finite total curvature, of both genus zero and higher genus. In the genus zero case, we classify all such surfaces with at most $2n+1$ ends, and with symmetry…

We characterize the quasiprojective groups that appear as fundamental groups of compact $3$-manifolds (with or without boundary). We also characterize all closed $3$-manifolds that admit good complexifications. These answer questions of…

Suppose that $\Gamma$ is a non-empty connected graph, $\mathfrak{G}$ is the fundamental group of a graph of groups over $\Gamma$, and $\mathcal{C}$ is a root class of groups (the last means that $\mathcal{C}$ contains non-trivial groups and…

A topological group G is profinite if it is compact and totally disconnected. Equivalently, G is the inverse limit of a surjective system of finite groups carrying the discrete topology. We discuss how to represent a countably based…

We prove that any group $G$ occurs as $\E(X)$, where $X$ is CW-complex of finite dimension and $\E(X)$ denotes its group of self-homotopy equivalence. Thus, we generalize a well know-theorem due to Costoya and Viruel \cite{CV} asserting…

A countable group is residually finite if every nontrivial element can act nontrivially on a finite set. When a group fails to be residually finite, we might want to measure how drastically it fails - it could be that only finitely many…

We prove that the group of homotopy classes of relative homotopy automorphisms of a simply connected finite CW-complex is finitely presented and that the rationalization map from this group to its rational analogue has a finite kernel.

Let G be a connected complex Lie group. We show that any flat principal G-bundle over any finite CW-complex pulls back to a trivial bundle over some finite covering space of the base space if and only if each real characteristic class of…

Suppose $G$ is a finitely generated infinite group, and $\mathcal G$ is a graph of groups decomposition of $G$ such that the edge groups are finite. This paper establishes that the topology of the Floyd boundary of $G$ is uniquely…

A {\it graph product} $G$ on a graph $\Gamma$ is a group defined as follows: For each vertex $v$ of $\Gamma$ there is a corresponding non-trivial group $G_v$. The group $G$ is the quotient of the free product of the $G_v$ by the commutation…

We give a finite presentation of the mapping class group of an oriented (possibly bounded) surface of genus greater or equal than 1, considering Dehn twists on a very simple set of curves.

Let $p$ be a prime and let $\mathbb{C}$ be the complex field. We explicitly classify the finite solvable irreducible monomial subgroups of $\mathrm{GL}(p,\mathbb{C})$ up to conjugacy. That is, we give a complete and irredundant list of…

If $G$ is a group and $S$ a generating set, $G$ canonically embeds into the automorphism group of its Cayley graph and it is natural to try to minimize, over all generating sets, the index of this inclusion. This infimum is called the…

Let G be a finite group and S a subset of G\{0}. We call S an additive basis of G if every element of G can be expressed as a sum over a nonempty subset in some order. Let cr(G) be the smallest integer t such that every subset of G\{0} of…

The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a…

We define a `nice representation' of a finitely presented group G as being a non-degenerate essentially surjective simplicial map f from a `nice' space X into a 3-complex associated to a presentation of G, with a strong control over the…

Given a finitely generated linear group $G$ over $\mathbb{Q}$, we construct a simple group $\Gamma$ that has the same finiteness properties as $G$ and admits $G$ as a quasi-retract. As an application, we construct a simple group of type…

Let S be a generating set of a group G. We say that G has FINITE WIDTH relative to S if G=(S\cup S^{-1})^k for a suitable natural number k. We say that a group G is a group of FINITE C-WIDTH if G has finite width with respect to all…

Let $G$ be a finite group. An element $g$ of $G$ is called a vanishing element if there exists an irreducible character $\chi$ of $G$ such that $\chi(g) = 0$; in this case, we say that the conjugacy class of $g$ is a vanishing conjugacy…