63 citations · 280 across the 35 of their papers we have counts for
22 papers · 1 filter
A trace pairing and Elliott invariant for groupoid homology
Robin Deeley, Rufus Willett
For an étale groupoid, we define a pairing between the Crainic-Moerdijk groupoid homology and the simplex of invariant Borel probability measures on the base space. The main novelt…
Embeddings of von Neumann algebras into uniform Roe algebras and quasi-local algebras
Florent P. Baudier, Bruno de Mendonça Braga, Ilijas Farah +2
We study which von Neumann algebras can be embedded into uniform Roe algebras and quasi-local algebras associated to a uniformly locally finite metric space . Under weak assumpt…
-algebras with finite complexity
Arturo Jaime, Rufus Willett
Complexity rank for -algebras was introduced by the second author and Yu for applications towards the UCT: very roughly, this rank is at most if you can repeatedly cut the…
Uniform Roe algebras of uniformly locally finite metric spaces are rigid
Florent P. Baudier, Bruno de Mendonça Braga, Ilijas Farah +3
We show that if and are uniformly locally finite metric spaces whose uniform Roe algebras, $\cstu(X)$ and $\cstu(Y)$, are isomorphic as \cstar-algebras, then and ar…
The UCT for -algebras with finite complexity
Rufus Willett, Guoliang Yu
A -algebra satisfies the Universal Coefficient Theorem (UCT) of Rosenberg and Schochet if it is equivalent in Kasparov's -theory to a commutative -algebra. This paper…
Dynamic asymptotic dimension and Matui's HK conjecture
Christian Bönicke, Clément Dell'Aiera, James Gabe +1
We prove that the homology groups of a principal ample groupoid vanish in dimensions greater than the dynamic asymptotic dimension of the groupoid (as a side-effect of our methods,…