4 papers
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…
Functoriality of real crossed product K-theory spectral sequences with respect to group homomorphisms
Jeffrey L. Boersema, Sarah L. Browne, Elizabeth Gillaspy +1
Spectral sequences are a key tool for computing the K-theory of a crossed product C-algebra. However, the impact of a group homomorphism on such a spectral se…
Invariant measures and traces on groupoid -algebras
Alistair Miller, Eduardo Scarparo
We provide sufficient conditions for the existence of a trace on the essential -algebra of a (not necessarily Hausdorff) étale groupoid which extends an invari…
Homology and K-theory for self-similar actions of groups and groupoids
Alistair Miller, Benjamin Steinberg
Nekrashevych associated to each self-similar group action an ample groupoid and a -algebra. We perform complete computations of the homology of the groupoid and th…