具有 Spanier-Whitehead 对偶性的群
Groups with Spanier-Whitehead duality
AI总结：
本文基于 Kasparov 的工作研究离散群的 Spanier-Whitehead K-对偶性，通过标准“gamma 元素”技术与 property gamma 循环方法构造对偶类，将其与 Baum-Connes 猜想比较，并证明了一大类群的对偶性。
摘要：
基于 Kasparov 的工作，我们研究离散群的 Spanier-Whitehead K-对偶概念。它被定义为自然附属于该群的两个 C*-代数（即约化群 C*-代数与群作用在真作用泛例子上的交叉积）之间的 KK-范畴对偶性。我们通过基于两种方法（标准“gamma 元素”技术与基于具有 property gamma 的循环的较新方法）构造对偶类，将该概念与 Baum-Connes 猜想进行比较。作为分析结果，我们证明了一大类群的 Spanier-Whitehead 对偶性，包括 Bieberbach 空间群、作用在树上的群以及 Lorentz 群中的格。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
