Almost finiteness, comparison, and Z-stability

David Kerr (Texas A&M University)

Friday 9th February, 2018 13:00-14:00 Maths 311B

Abstract

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 formulate a notion of almost finiteness for group actions on compact spaces which can be seen as an analogue of both hyperfiniteness in the measure-preserving setting and of Z-stability in the C*-algebra setting and is related to dynamical comparison in the same way that 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 Z-stable, which leads to new examples of classifiable crossed products.

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