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math.OA2024
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…
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…