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math.KT2026
Discretisation and independent resolutions of ample groupoids
Xin Li, Alistair Miller
We develop a general framework for understanding and computing both the groupoid homology of an ample groupoid and the topological K-theory of its reduced C*-algebra, based on two…
math.KT2024
Isomorphisms in K-theory from isomorphisms in groupoid homology theories
Alistair Miller
We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid homology induced by an étale correspondence yields an isomorphism in the K-theory of the associa…
math.KT2023
Ample groupoid homology and étale correspondences
Alistair Miller
We show that étale correspondences between ample groupoids induce homomorphisms of homology groups. To complement this we explore the module categories of ample groupoids. We const…