16 citations · 49 across the 11 of their papers we have counts for
11 papers
Chern character for torsion-free ample groupoids
Valerio Proietti, Makoto Yamashita
For an ample groupoid with torsion-free stabilizers, we construct a Chern character map going from the domain of the Baum-Connes assembly map of G to the Crainic-Moerdijk homology…
Hofstadter-Toda spectral duality and quantum groups
Pasquale Marra, Valerio Proietti, Xiaobing Sheng
The Hofstadter model allows to describe and understand several phenomena in condensed matter such as the quantum Hall effect, Anderson localization, charge pumping, and flat-bands…
Homology and K-theory of dynamical systems. IV. Further structural results on groupoid homology
Valerio Proietti, Makoto Yamashita
We consider the homology theory of étale groupoids introduced by Crainic and Moerdijk, with particular interest to groupoids arising from topological dynamical systems. We prove a…
A geometric Elliott invariant and noncommutative rigidity of mapping tori
Hao Guo, Valerio Proietti, Hang Wang
We prove a rigidity property for mapping tori associated to minimal topological dynamical systems using tools from noncommutative geometry. More precisely, we show that under mild…
Homology and K-theory of dynamical systems III. Beyond stably disconnected Smale spaces
Valerio Proietti, Makoto Yamashita
We study homological invariants of étale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolu…
Categorical approach to the Baum-Connes conjecture for étale groupoids
Christian Bönicke, Valerio Proietti
We consider the equivariant Kasparov category associated to an étale groupoid, and by leveraging its triangulated structure we study its localization at the "weakly contractible" o…
Homology and K-theory of dynamical systems. II. Smale spaces with totally disconnected transversal
Valerio Proietti, Makoto Yamashita
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 space wi…
Homology and K-theory of dynamical systems. I. torsion-free ample groupoids
Valerio Proietti, Makoto Yamashita
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) groupoid…
Groups with Spanier-Whitehead duality
Shintaro Nishikawa, Valerio Proietti
Building on work by Kasparov, we study the notion of Spanier-Whitehead K-duality for a discrete group. It is defined as duality in the KK-category between two C*-algebras which are…
A note on homology for Smale spaces
Valerio Proietti
We collect three observations on the homology for Smale spaces defined by Putnam. The definition of such homology groups involves four complexes. It is shown here that a simple con…
Index theory on the Miščenko bundle
Jens Kaad, Valerio Proietti
We consider the assembly map for principal bundles with fiber a countable discrete group. We obtain an index-theoretic interpretation of this homomorphism by providing a tensor-pro…