21 citations · 49 across the 16 of their papers we have counts for
18 papers
Triangulating surfaces quasi-isometrically
Agelos Georgakopoulos, Federico Vigolo
We prove that if a complete Riemannian surface is quasi-isometric to some bounded degree graph , then admits a triangulation whose 1-skeleton is quasi-isometric to…
On automorphisms, quasimorphisms, and coarse automorphisms of acylindrically hyperbolic groups
Ashot Minasyan, Alessandro Sisto, Federico Vigolo
We investigate the action of the automorphism group of an acylindrically hyperbolic group G on its space of homogeneous quasimorphisms, and identify its kernel with the subgroup of…
Coarse Baum-Connes and warped cones: failure of surjectivity in odd degree
Christos Kitsios, Thomas Schick, Federico Vigolo
We prove a conjecture of Roe by constructing unified warped cones that violate the coarse Baum-Connes conjecture. Interestingly, the reason for this is probably not what Roe expect…
C*-rigidity of bounded geometry metric spaces
Diego Martínez, Federico Vigolo
We prove that uniformly locally finite metric spaces with isomorphic Roe algebras must be coarsely equivalent. As an application, we also prove that the outer automorphism group of…
On a coarse invertibility spectrum for coarse groups
Leo Schäfer, Federico Vigolo
We introduce a coarse algebraic invariant for coarse groups and use it to differentiate various coarsifications of the group of integers. This lets us answer two questions posed by…
A rigidity framework for Roe-like algebras
Diego Martínez, Federico Vigolo
In this memoir we develop a framework to study rigidity problems for Roe-like C*-algebras of countably generated coarse spaces. The main goal is to give a complete and self-contain…
Roe algebras of coarse spaces via coarse geometric modules
Diego Martínez, Federico Vigolo
We provide a construction of Roe (C*-)algebras of general coarse spaces in terms of coarse geometric modules. This extends the classical theory of Roe algebras of metric spaces and…
Dynamical propagation and Roe algebras of warped spaces
Tim de Laat, Federico Vigolo, Jeroen Winkel
Given a non-singular action , we define the -algebra of operators of finite dynamical propagation associated w…
An Invitation to Coarse Groups
Arielle Leitner, Federico Vigolo
In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as…
A Markovian and Roe-algebraic approach to asymptotic expansion in measure
Kang Li, Federico Vigolo, Jiawen Zhang
In this paper, we conduct further studies on geometric and analytic properties of asymptotic expansion in measure. More precisely, we develop a machinery of Markov expansion and ob…
Asymptotic expansion in measure and strong ergodicity
Kang Li, Federico Vigolo, Jiawen Zhang
In this paper, we introduce and study a notion of asymptotic expansion in measure for measurable actions. This generalises expansion in measure and provides a new perspective on th…
Remarks on partitions into expanders
Federico Vigolo
In this note we give a short proof that graphs having no linearly small Følner sets can be partitioned into a union of expanders. We use this fact to prove a partition result for g…
On the structure of asymptotic expanders
Ana Khukhro, Kang Li, Federico Vigolo +1
In this paper, we use geometric tools to study the structure of asymptotic expanders and show that a sequence of asymptotic expanders always admits a "uniform exhaustion by expande…
A new construction of CAT(0) cube complexes
Robert Kropholler, Federico Vigolo
We introduce the notion of coupled link cube complex (CLCC) as a means of constructing interesting cocompactly cubulated groups. CLCCs are defined locally, making them a useful too…
Fundamental groups as limits of discrete fundamental groups
Federico Vigolo
In this note we investigate to what extent the fundamental group of a metric space can be described as the inverse limit of its discrete fundamental groups. We show that some mild…
Discrete fundamental groups of Warped Cones and expanders
Federico Vigolo
In this paper we compute the discrete fundamental groups of warped cones. As an immediate consequence, this allows us to show that there exist coarsely simply-connected expanders a…
Superexpanders from group actions on compact manifolds
Tim de Laat, Federico Vigolo
It is known that the expanders arising as increasing sequences of level sets of warped cones, as introduced by the second-named author, do not coarsely embed into a Banach space as…
Measure expanding actions, expanders and warped cones
Federico Vigolo
We define a way of approximating actions on measure spaces using finite graphs; we then show that in quite general settings these graphs form a family of expanders if and only if t…