群胚的粗上同调和Connes-Chern特征映射

Coarse groupoid cohomology and Connes-Chern character

本文引入群胚上粗上同调群的概念,构造了一个从群胚粗上同调群映到群胚Roe*-代数循环上同调群的Connes-Chern特征映射.作为例子,本文构造了平坦G-主丛所定义的和乐(holonomy)群胚上的一个粗上同调类.

We introduce the concept of coarse groupoid cohomology for a groupoid equipped with a coarse structure. We construct a Connes-Chern character map from the coarse groupoid cohomology to the cyclic cohomology of the smooth coarse Roe algebra of the groupoid. As an example, we construct a cyclic coarse cocycle on the holonomy groupoid associated to a flat principal G-bundle for a Lie group G.