Coarse assembly maps

U. Bunke, A. Engel
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引用次数: 17

Abstract

A coarse assembly map relates the coarsification of a generalized homology theory with a coarse version of that homology theory. In the present paper we provide a motivic approach to coarse assembly maps. To every coarse homology theory $E$ we naturally associate a homology theory $E\mathcal{O}^{\infty}$ and construct an assembly map $$\mu_{E} :\mathrm{Coarsification}(E\mathcal{O}^{\infty})\to E\ .$$ For sufficiently nice spaces $X$ we relate the value $E\mathcal{O}^{\infty}(X)$ with the locally finite homology of $X$ with coefficients in $E(*)$. In the example of coarse $K$-homology we discuss the relation of our motivic constructions with the classical constructions using $C^{*}$-algebra techniques.
粗装配图
一个粗装配图将一个广义同调理论的粗化与该同调理论的粗化版本联系起来。在本文中,我们提供了一种动机方法来处理粗装配图。对于每一个粗糙的同调理论$E$,我们自然地关联一个同调理论$E\mathcal{O}^{\infty}$并构造一个装配映射$$\mu_{E} :\mathrm{Coarsification}(E\mathcal{O}^{\infty})\to E\ .$$对于足够好的空间$X$,我们将值$E\mathcal{O}^{\infty}(X)$与$X$的局部有限同调与$E(*)$中的系数联系起来。在粗糙$K$ -同调的例子中,我们用$C^{*}$ -代数技术讨论了我们的动机结构与经典结构的关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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