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arXiv · 1908.03749

Groups with Spanier-Whitehead duality

Shintaro Nishikawa·Valerio Proietti
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Abstract

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.

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BibTeXRIS

Shintaro Nishikawa, Valerio Proietti. 2019-08-10. Groups with Spanier-Whitehead duality. https://doi.org/10.2140/akt.2020.5.465

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