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• 天元讲堂（6.15）：Dimension, comparison, and almost finiteness
• 浏览量：292 发布人：佚名 发布时间：2017-06-15 15:55:32
• 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.