Zobrazeno 1 - 10
of 41
pro vyhledávání: '"Proietti, Valerio"'
Publikováno v:
J. Math. Phys. 65, 071903 (2024)
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 in quasiperiodic structures, and is a rare example of fractality in th
Externí odkaz:
http://arxiv.org/abs/2312.14242
Autor:
Proietti, Valerio, Yamashita, Makoto
We consider the homology theory of \'etale groupoids introduced by Crainic and Moerdijk, with particular interest to groupoids arising from topological dynamical systems. We prove a K\"unneth formula for products of groupoids and a Poincar\'e-duality
Externí odkaz:
http://arxiv.org/abs/2310.09928
Publikováno v:
Journal of Functional Analysis 287-11 (2024), 110625
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 geometric assumptions, an orientation-preserving leafwise homotopy equ
Externí odkaz:
http://arxiv.org/abs/2207.06840
Autor:
Proietti, Valerio, Yamashita, Makoto
We study homological invariants of \'etale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology groups defin
Externí odkaz:
http://arxiv.org/abs/2207.03118
Autor:
Bönicke, Christian, Proietti, Valerio
We consider the equivariant Kasparov category associated to an \'etale groupoid, and by leveraging its triangulated structure we study its localization at the "weakly contractible" objects, extending previous work by R. Meyer and R. Nest. We prove th
Externí odkaz:
http://arxiv.org/abs/2202.08067
Publikováno v:
In Journal of Functional Analysis 1 December 2024 287(11)
Autor:
Proietti, Valerio, Yamashita, Makoto
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 with totally disconnected stable sets, and prove that the associated spe
Externí odkaz:
http://arxiv.org/abs/2104.10938
Autor:
Proietti, Valerio, Yamashita, Makoto
Publikováno v:
Ergodic Theory and Dynamical Systems 42-8 (2022), 2630-2660
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 C*-algebra, provided the groupoid has torsion-free stabilizers and sa
Externí odkaz:
http://arxiv.org/abs/2006.08028
Autor:
Nishikawa, Shintaro, Proietti, Valerio
Publikováno v:
Ann. K-Th. 5 (2020) 465-500
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 naturally attached to the group, namely the reduced group C*-algebra
Externí odkaz:
http://arxiv.org/abs/1908.03749
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