The asymptotic dimension theory was founded by Gromov [M. Gromov, Asymptotic invariants
of infinite groups, in: Geometric Group Theory, vol. 2, Sussex, 1991, in: London Math. Soc …

We introduce a geometric invariant, called finite decomposition complexity (FDC), to study
topological rigidity of manifolds. We prove for instance that if the fundamental group of a …

Given a function f: X→ Y of metric spaces, the classical Hurewicz theorem states that dim
(X)≤ dim (f)+ dim (Y). We provide analogs of this theorem for the Assouad–Nagata …

In an earlier work we introduced a geometric invariant, called finite decomposition
complexity (FDC), to study topological rigidity of manifolds. In particular, we proved the …

We propose two definitions of configuration Lie groupoids and in both the cases we prove a
Fadell-Neuwirth type fibration theorem for a class of Lie groupoids. We show that this is the …

We develop the foundations of a geometric theory of countably-infinite approximate groups,
extending work of Bj\" orklund and the second-named author. Our theory is based on the …

On asymptotic dimension of countable Abelian groups Page 1 Topology and its
Applications 153 (2006) 2047–2054 www.elsevier.com/locate/topol On asymptotic …

Abstract Coarse spaces [26] and balleans [23] are known to be equivalent constructions
([25]). The main subject of this paper is the category, Coarse, having as objects these …

We initiate a quantitative study of measure equivalence (and orbit equivalence) between
finitely generated groups, which extends the classical setting of Lp measure equivalence. In …

The, large scale, or coarse perspective on the geometry of metric spaces plays an important
role in approaches to conjectures in operator algebras and the topology of manifolds …