Dynamic asymptotic dimension and groupoid homology

Christian Bonicke  (University of Glasgow)

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


Dynamic asymptotic dimension is a dimension theory for group actions and more generally for ¨¦tale 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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