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

2024/02/09 by Deeley, Robin J., Willett, Rufus · 1 citation
#22A22 #46L80 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2402.06837

Abstract

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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• Chern character for torsion-free ample groupoids

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