1 citations · 1 across the 7 of their papers we have counts for
7 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…
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…
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…
Functors between Kasparov categories from étale groupoid correspondences
Alistair Miller
For an étale correspondence of étale groupoids, we construct an induction functor between equivariant Kaspa…