度量空间的大尺度几何与高指标问题

Large Scale Geometry of Metric Spaces and Higher Index Problems

粗几何上的指标理论是"非交换几何"领域近年来非常活跃的研究分支,与几何、拓扑、算子代数、几何群论、Banach空间几何理论等都有密切联系。对该领域的若干思想、主要问题和部分最新研究进展进行综述性介绍。

Index theories associated with coarse geometry is one of the most active research areas in Noncommutative Geometry.It has close connections to geometry,topology,operator algebras,geometric group theory,Banach space geometry,etc..In this article,a brief survey to some of the key ideas,formulation of the main problems,and some recent important progress in this area are given.