We consider asymptotic dimension of coarse spaces. We analyse coarse structures induced by metrisable compactifications. We calculate asymptotic dimension of coarse cell complexes. We calculate the… Expand

We study uniform and coarse embeddings between Banach spaces and topological groups. A particular focus is put on equivariant embeddings, that is, continuous cocycles associated to continuous affine… Expand

In this paper we classify countable locally finite-by-abelian groups up to coarse isomorphism. This classification is derived from a coarse classification of amenable shift-homogeneous metric spaces.

We construct the first example of a coarsely non-amenable (= without Guoliang Yu’s property A) metric space with bounded geometry which coarsely embeds into a Hilbert space.

We consider asymptotic dimension in the general setting of coarse spaces and prove some basic properties such as monotonicity, a formula for the asymptotic dimension of finite unions and estimates… Expand

We prove that every visual Gromov hyperbolic space X whose boundary at infinity has the finite capacity dimension n admits a quasi-isometric embedding into (n+1)-fold product of metric trees.