Group-theoretic compactification of Bruhat–Tits buildings
Group-theoretic conditions under which closed aspherical manifolds are covered by Euclidean space
Hass, Rubinstein, and Scott showed that every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. This theorem does not generalize to higher dimensions. However, we provide geometric tools with which variations of this theorem can be proved in all dimensions.
Growth functions and automatic groups.
Growth functions for some uniformly amenable groups
We present a simple constructive proof of the fact that every abelian discrete group is uniformly amenable. We improve the growth function obtained earlier and find the optimal growth function in a particular case. We also compute a growth function for some non-abelian uniformly amenable group.
Growth in