We prove an analogue of the Baum–Connes conjecture for free orthogonal quantum groups.
More precisely, we show that these quantum groups have a γ-element and that γ= 1. It …

We consider the equivariant Kasparov category associated to an étale groupoid, and by
leveraging its triangulated structure we study its localization at the 'weakly …

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 …

Given an ample groupoid, we construct a spectral sequence with groupoid homology with
integer coefficients on the second sheet, converging to the K-groups of the (reduced) …

In this paper we study the K-theory of free quantum groups in the sense of Wang and Van
Daele, more precisely, of free products of free unitary and free orthogonal quantum groups …

We carefully define and study C*-algebras over topological spaces, possibly non-Hausdorff,
and review some relevant results from point-set topology along the way. We explain the …

Non-commutative topology deals with topological properties of C*-algebras. Already in the
1970s, the classification of AF-algebras by K-theoretic data [15] and the work of Brown …

We apply our previous work on the relation between groupoid homology and K-theory to
Smale spaces. More precisely, we consider the unstable equivalence relation of a Smale …

We study the theory of projective representations for a compact quantum group $\mathbb {G}
$, ie actions of $\mathbb {G} $ on $\mathcal {B}(H) $ for some Hilbert space $ H $. We show …

We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid
homology induced by an\'etale correspondence yields an isomorphism in the K-theory of the …