Dynamic asymptotic dimension and groupoid homology

Christian Bonicke  (University of Glasgow)

16:00-17:00, October 18, 2021   Zoom 93974276120 (Passcode: 506851)

Abstract:

Dynamic asymptotic dimension is a dimension theory for group actions and more generally for étale groupoids developed by Guentner, Willett, and Yu, which generalizes Gromov’s theory of asymptotic dimension. Having finite asymptotic dimension is known to have important implications for the structure of the associated C*-algebras. In this talk I will report on recent joint work with Dell’Aiera, Gabe, and Willett in which we prove a homology vanishing result for groupoids with finite dynamic asymptotic dimension. We also investigate the relation between groupoid homology and the K-theory of the groupoid C*-algebra, a topic which received a lot of attention in recent years following a conjecture by Matui.

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