Fiberwise amenability and almost elementariness for étale groupoids

Abstract: In this talk, I will discuss two new properties for locally compact Hausdorff étale 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.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( slides | video )

Noncommutative Geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click sju.webex.com/meet/nikolaei (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.