Fiberwise amenability and almost elementariness for etale groupoids

Xin Ma (The University of Memphis)

10:00-11:00, October 26, 2021   Tencent Meeting 716705858


In this talk, I will discuss two new properties for locally compact Hausdorff etale groupoids. One is from a coarse geometric view called fiberwise amenability. Another one is called almost elementariness, which is a new finite-dimensional approximation property. I will explain how these notions related to almost finiteness defined by Matui and refined by Kerr and show our almost elementariness implying tracial Z-stability of reduced groupoid C*-algebras. As an application. This implies that Matui's almost finiteness in the groupoid setting also implies Z-stability when the groupoid is minimal 2nd countable and topological amenable. This was open in general before. I will also present more applications if time permits. This is based on joint work with Jianchao Wu.

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