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The rational HK-conjecture: transformation groupoids and a revised version

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arxiv 2402.06837 v1 pith:LAZJM5UF submitted 2024-02-09 math.KT math.OA

Robin J. Deeley , Rufus Willett This is my paper · ORCID
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keywords hk-conjecturerationalgroupoidsrevisedtransformationversioncaseclass
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We prove the rational HK-conjecture for a large class of transformation groupoids in the case when the relevant action has torsion-free stabilizers. A revised version of the rational HK-conjecture in the case of (possibly) torsion stabilizers is introduced and proved for a large class of transformation groupoids. In particular, this revised version holds for Scarparo's counterexamples to the original rational HK-conjecture. The key tools used are the Baum-Connes conjecture and a Chern character defined by Raven.

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    An etale groupoid's invariant measures pair canonically with its zeroth Crainic-Moerdijk homology, yielding a groupoid Elliott invariant shown to match the C*-algebraic Elliott invariant for many integer actions and o...

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