Browsing by Author "Proietti, Valerio"

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Groups with Spanier-Whitehead Duality

[OWP-2019-23] Nishikawa, Shintaro; Proietti, Valerio (Mathematisches Forschungsinstitut Oberwolfach, 2019-09-17)

We introduce the notion of Spanier-Whitehead $K$ -duality for a discrete group $G$ , defined as duality in the KK-category between two $C*$ -algebras which are naturally attached to the group, namely the reduced group ...
Homology and $K$ -Theory of Torsion-Free Ample Groupoids and Smale Spaces

[OWP-2020-20] Proietti, Valerio; Yamashita, Makoto (Mathematisches Forschungsinstitut Oberwolfach, 2020-10-09)

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 groupoid C*-algebra when the groupoid has torsion-free ...