论文标题
Smale空间KK二维的基本类别的几何代表
A geometric representative for the fundamental class in KK-duality of Smale spaces
论文作者
论文摘要
非共同几何程序中的一种基本要素是KK二元性的概念，通常称为K TheoreticPoincaré二元性，它概括了Spanter-white-whitehead二元性。在本文中，我们构建了一个$θ$ -Summable的Fredholm模块，该模块代表了Smale空间的稳定和不稳定的Ruelle代数之间的KK二次基础类别。为了找到这样的代表，我们在用高度控制的Lipschitz常数上构建了统一的动态分区。这需要对鲍恩的马尔可夫分区进行概括。除了一种十分点采样技术，我们产生了惠特尼嵌入定理的非交通类似物，导致了弗雷德·霍尔姆模块。
A fundamental ingredient in the noncommutative geometry program is the notion of KK-duality, often called K-theoretic Poincaré duality, that generalises Spanier-Whitehead duality. In this paper we construct a $θ$-summable Fredholm module that represents the fundamental class in KK-duality between the stable and unstable Ruelle algebras of a Smale space. To find such a representative, we construct dynamical partitions of unity on the Smale space with highly controlled Lipschitz constants. This requires a generalisation of Bowen's Markov partitions. Along with an aperiodic point-sampling technique we produce a noncommutative analogue of Whitney's embedding theorem, leading to the Fredholm module.
