Finitely summable $γ$-elements for word-hyperbolic groups

高秩群与格上的可和Fredholm模

Finitely summable Fredholm modules over higher rank groups and lattices

给出了高阶群和格上的可和Fredholm表示（Fredholm模）的一个完整分类（直到光滑同伦）。我们的结果是一个直接后果的工作巴德，弗曼，Gelander和莫诺的概括Kazhdan的性质T的局部紧群。

有限可和 $K$-同调、指标配对与 Cantor 极小系统

Finitely Summable $K$-homology, the Index Pairing, and Cantor Minimal Systems

本文研究 Cantor 极小系统交叉积 $C^*$-代数的指标配对，利用 Putnam 轨道破缺 AF-子代数证明可通过 Connes 迹公式计算任意配对，并证明里程计代数具有一致有限可和 $K$-同调。

双曲群边界作用的可和Fredholm模

Finitely summable Fredholm modules for boundary actions of hyperbolic groups

在交叉积C* 代数$C(\bd \G)\rtimes \G$上构造了一族与非初等双曲群$\G$在其Gromov边界$\bd \G$上的作用相关的奇可和Fredholm模.这些Fredholm模都代表了K-同调中相同的、特殊的类，即与$\G$的Gromov紧化相关联的$C(\bd \G)\rtimes \G$的“边界扩张”，并且通常是非零的。它们的可和性与边界的豪斯多夫维数密切相关。利用这些结果计算了循环上同调边界扩张的Connes-Chern特征标。

On finitely summable Fredholm modules from Smale spaces

We prove that all K-homology classes of the stable (and unstable) Ruelle algebra of a Smale space have explicit Fredholm module representatives that are finitely summable on the same smooth subalgebra and with the same degree of summability. The smooth subalgebra is induced by a metric on the underlying Smale space groupoid and fine transversality relations between stable and unstable sets. The degree of summability is related to the fractal dimension of the Smale space. Further, the Fredholm modules are obtained by taking Kasparov products with a fundamental class of the Spanier-Whitehead K-d…

配对的代数K理论不变性结果

Invariance results for pairings with algebraic K-theory

对于复数上的每个代数，我们以逆变函子的方式将一列阿贝尔群联系起来。在（m-1）阶上，我们得到了代数模稳定的m-可和扰动上的m-可和Fredholm模.这些新的可重和的K-同调群与循环同调和代数K理论配对。在循环同调的情况下，配对由Chern-Connes特征诱导。由Connes-Karoubi乘法特征标导出了代数K理论与可积可和K同调之间的配对关系。

Local cyclic homology of group Banach algebras I: Hyperbolic groups

We calculate the bivariant local cyclic cohomology of the Banach convolution algebra of summable functions on a word-hyperbolic group. Our result implies that the Banach algebraic assembly map in local cyclic homology is an isomorphism for such a group.