Groups with Spanier-Whitehead duality

Fuente: arXiv
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Hauptverfasser: Nishikawa, Shintaro, Proietti, Valerio
Format: Preprint
Veröffentlicht: 2019
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author Nishikawa, Shintaro
Proietti, Valerio
author_facet Nishikawa, Shintaro
Proietti, Valerio
contents 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 and the crossed product for the group action on the universal example for proper actions. We compare this notion to the Baum-Connes conjecture by constructing duality classes based on two methods: the standard "gamma element" technique, and the more recent approach via cycles with property gamma. As a result of our analysis, we prove Spanier-Whitehead duality for a large class of groups, including Bieberbach's space groups, groups acting on trees, and lattices in Lorentz groups.
format Preprint
id arxiv_https___arxiv_org_abs_1908_03749
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle Groups with Spanier-Whitehead duality
Nishikawa, Shintaro
Proietti, Valerio
K-Theory and Homology
Operator Algebras
46L85 (Primary) 46L80, 55P25 (Secondary)
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 and the crossed product for the group action on the universal example for proper actions. We compare this notion to the Baum-Connes conjecture by constructing duality classes based on two methods: the standard "gamma element" technique, and the more recent approach via cycles with property gamma. As a result of our analysis, we prove Spanier-Whitehead duality for a large class of groups, including Bieberbach's space groups, groups acting on trees, and lattices in Lorentz groups.
title Groups with Spanier-Whitehead duality
topic K-Theory and Homology
Operator Algebras
46L85 (Primary) 46L80, 55P25 (Secondary)
url https://arxiv.org/abs/1908.03749