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 …

In this paper, we introduce properties including groupoid comparison, pure infiniteness, and
paradoxical comparison as well as a new algebraic tool called groupoid semigroup for …

ON TRACIAL Z-STABILITY OF SIMPLE NON-UNITAL C∗-ALGEBRAS Introduction The Jiang-Su
algebra Z has become a cornerstone in the cl Page 1 ON TRACIAL Z-STABILITY OF SIMPLE …

We introduce diagonal comparison, a regularity property of diagonal pairs where the sub-C*-
algebra has totally disconnected spectrum, and establish its equivalence with the …

In this paper we show that for an almost finite minimal ample groupoid G, its reduced C^* C∗-
algebra C_r^*(G) C r∗(G) has real rank zero and strict comparison even though C_r^*(G) C …

Let $\mathcal {G} $ be a locally compact $\sigma $-compact Hausdorff ample groupoid on a
compact space. In this paper, we further examine the (ubiquitous) fiberwise amenability …

Three important properties of groups, amenability, Property A and almost finiteness, are in
our focus, in the wider context of general countable bounded degree graphs. A graph is …

Let $\mathcal {G} $ be a locally compact Hausdorff\'{e} tale groupoid. We call a tracial state
$\tau $ on a general groupoid $ C^* $-algebra $ C_\nu^*(\mathcal {G}) $ canonical if …

We introduce diagonal dimension, a version of nuclear dimension for diagonal sub-C*-
algebras (sometimes also referred to as diagonal C*-pairs). Our concept has good …

We develop our understanding of topological full groups, a way of constructing examples of
infinite simple groups with finiteness properties from ample groupoids. Our results are …