Fiberwise amenability and almost elementariness for etale groupoids

Xin Ma (University of Memphis)

Thursday 10th February, 2022 16:00-17:00 Maths 311B


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 for reduced groupoid C*-algebras. As an application, 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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