Related papers: Topics in geometric group theory, Part II
This is the second of a Series of three papers, the first one published in Geom Dedicata 167 p. 91-121 (2013), proving that all finitely presented groups are QSF.
This is the third and last of three papers containing the complete proof that all finitely presented groups are QSF.
This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of…
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…
A survey of problems, conjectures, and theorems about quasi-isometric classification and rigidity for finitely generated solvable groups.
We show that every countable group embeds in a group of type $FP_2$.
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
In this note we prove that every finitely presented subgroup of a systolic group is itself systolic.
Let $\mathcal G$ denote the space of finitely generated marked groups. For any finitely generated group $G$, we construct a continuous, injective map $f$ from the space of subgroups $Sub(G)$ to $\mathcal G$ that sends conjugate subgroups to…
It was recently proven by Esnault, Shusterman and the second named author, that the \'etale fundamental group of a connected smooth projective variety over an algebraically closed field $k$ is finitely presented. In this note, we extend…
This expository article revolves around the question to find short presentations of finite simple groups. This subject is one of the most active research areas of group theory in recent times. We bring together several known results on…
We show that every finitely generated residually finite torsion group $G$ embeds in a finitely generated torsion group $\Gamma$ that is residually finite simple. In particular we show the existence of finitely generated infinite torsion…
We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.
A finitely presented group is weakly geometrically simply connected (wgsc) if it is the fundamental group of some compact polyhedron whose universal covering is wgsc i.e. it has an exhaustion by compact connected and simply connected…
A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…
Given any finitely presented group G we find a triangular algebra such that has two presentations, one with fundamental group G and another with trivial group. Thus proving that given a collection G1,...,Gn of finitely presented groups…
The genus spectrum of a finite group $G$ is the set of all $g\geq 2$ such that $G$ acts faithfully and orientation-preserving on a closed compact orientable surface of genus $g$. This article is an overview of some results relating 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…
A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.
Universality has been an important concept in computable structure theory. A class $\mathcal{C}$ of structures is universal if, informally, for any structure, of any kind, there is a structure in $\mathcal{C}$ with the same…