Homological dimension of elementary amenable groups

Non-elementary amenable subgroups of automata groups

We consider groups of automorphisms of locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. This covers all known examples of groups that are not elementary amenable and act on the trees: groups of intermediate growths and Basilica group, by giving a more straightforward proof. Moreover, we deduce that all finitely generated branch groups ...

Recurrent Points and Discrete Points for Elementary Amenable Groups

Let fig be the Stone-Cech compactification of a group G, Aa the set of all almost periodic points in G, Ka c[U { supp eLIM(G)}] and Ra the set of all recurrent points in fiG. In this paper we will study the relationships between Ka and Ra, and between Aa and Ra. We will show that for any infinite elementary amenable group G, Aa Ra and RaKa =/= .

Lecture 9 : Elementary subexponentially amenable groups by Kate Juschenko

Groups of small homological dimension and the Atiyah Conjecture

A group has homological dimension ≤ 1 if it is locally free. We prove the converse provided that G satisfies the Atiyah Conjecture about L -Betti numbers. We also show that a finitely generated elementary amenable group G of cohomological dimension ≤ 2 possesses a finite 2dimensional model for BG and in particular that G is finitely presented and the trivial ZG-module Z has a 2-dimensional reso...

Homological Dimension and Critical Exponent of Kleinian Groups

We prove an inequality between the relative homological dimension of a Kleinian group Γ ⊂ Isom(Hn) and its critical exponent. As an application of this result we show that for a geometrically finite Kleinian group Γ, if the topological dimension of the limit set of Γ equals its Hausdorff dimension, then the limit set is a round sphere.