| Résume | Groupoid homology has attracted increasing attention from the topological dynamics and operator algebras communities following the work of Matui. Matui's HK conjecture predicts that the K-theory groups of the reduced C*-algebra of a minimal essentially principal ample groupoid coincides with its homology groups. We prove that homology of principal ample groupoids vanishes in degree above its dynamical asymptotic dimension, a notion of dimension from topological dynamics. We deduce several consequences: Matui's HK conjecture holds for low dimensional principal ample groupoids, and classification of their reduced C*-algebra. (Joint work with Christian Bonicke, Jamie Gabe and Rufus Willett) |
