6 papers
The rigidity problem for uniform Roe algebras
Alessandro Vignati
We solve the rigidity problem for uniform Roe algebras, by showing that two uniformly locally finite metric spaces with isomorphic uniform Roe algebras are bijectively coarsely equ…
A note on the quasi-local algebra of expander graphs
Bruno M. Braga, Ján Špakula, Alessandro Vignati
We show that the quasi-local algebra of a coarse disjoint union of expander graphs does not contain a Cartan subalgebra isomorphic to . N. Ozawa has recently shown tha…
Generic Compacta from Relations between Finite Graphs: Theory Building and Examples
Adam Bartoš, Tristan Bice, Alessandro Vignati
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relation…
Corona Rigidity
Ilijas Farah, Saeed Ghasemi, Andrea Vaccaro +1
We give a unified overview of the study of the effects of additional set theoretic axioms on quotient structures. Our focus is on rigidity, measured in terms of existence (or rathe…
Rigidity of Higson coronas
Alessandro Vignati
We show that under mild set theoretic hypotheses we have rigidity for algebras of continuous functions over Higson coronas, topological spaces arising in coarse geometry. In partic…
Constructing Compacta from Posets
Adam Bartoš, Tristan Bice, Alessandro Vignati
We develop a simple method of constructing topological spaces from countable posets with finite levels, one which applies to all second countable T_1 compacta. This results in a du…