报告题目：Dimension, comparison, and almost finiteness
报告人：David Kerr , Professor , Texas A&M University
报告时间：2017年6月15日下午16:30
报告地点：数学楼306
报告摘要：I will explain how one can develop a dynamical version of some of the theory surrounding the Toms-Winter conjecture for simple separable nuclear C*-algebras. In particular, I will introduce a notion of almost finiteness for group actions on compact spaces as an analogue of both hyperfiniteness in the measure-preserving setting and of $/mathcal{Z}$-stability in the C*-algebra setting. This generalizes Matui's concept of the same name from the zero-dimensional context and is related to dynamical comparison in the same way that $/mathcal{Z}$-stability is related to strict comparison in the Toms-Winter context. For free minimal actions of countably infinite groups on compact metrizable spaces the property of almost
finiteness implies that the crossed product is $/mathcal{Z}$-stable, which leads
to new examples of classifiable crossed products.