4 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 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…