A new description of equivariant cohomology for totally disconnected groups

Chern character for totally disconnected groups

In this paper we construct a bivariant Chern character for the equivariant KK-theory of a totally disconnected group with values in bivariant equivariant cohomology in the sense of Baum and Schneider. We prove in particular that the complexified left hand side of the Baum-Connes conjecture for a totally disconnected group is isomorphic to cosheaf homology. Moreover, it is shown that our transformation extends the Chern character defined by Baum and Schneider for profinite groups.

全不连通群的 Farrell-Jones 猜想的继承性质

Inheritance properties of the Farrell-Jones Conjecture for totally disconnected groups

研究全不连通群 Hecke 代数的 K 理论 Farrell-Jones 猜想，证明其对闭子群具有继承性，并为后续约化 p-adic 群情形建立构造与工具。

Independent resolutions for totally disconnected dynamical systems I: Algebraic case

This is the first out of two papers on independent resolutions for totally disconnected dynamical systems. In the present paper, we discuss independent resolutions from an algebraic point of view. We also present applications to group homology and cohomology. This first paper sets the stage for our second paper, where we explain how to use independent resolutions in K-theory computations for crossed products attached to totally disconnected dynamical systems.

Independent resolutions for totally disconnected dynamical systems II: C*-algebraic case

We develop the notion of independent resolutions for crossed products attached to totally disconnected dynamical systems. If such a crossed product admits an independent resolution of finite length, then its K-theory can be computed (at least in principle) by analysing the corresponding six-term exact sequences. Building on our previous paper on algebraic independent resolutions, we give a criterion for the existence of finite length independent resolutions. Moreover, we illustrate our ideas in various concrete examples.

动力系统的同调与 K-理论. II. 具有全不交截面的 Smale 空间

Homology and K-theory of dynamical systems. II. Smale spaces with totally disconnected transversal

本文将群胚同调与 K-理论关系应用于 Smale 空间，证明具有全不交稳定集的 Smale 空间相关谱序列在第二页展示 Putnam 稳定同调群，且该同调同构于不稳定等价关系的群胚同调。

Equivariant local cyclic homology and the equivariant Chern-Connes character

We define and study equivariant analytic and local cyclic homology for smooth actions of totally disconnected groups on bornological algebras. Our approach contains equivariant entire cyclic cohomology in the sense of Klimek, Kondracki and Lesniewski as a special case and provides an equivariant extension of the local cyclic theory developped by Puschnigg. As a main result we construct a multiplicative Chern-Connes character for equivariant KK-theory with values in equivariant local cyclic homology.