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arXiv · 2402.06837

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

Robin J. Deeley·Rufus Willett
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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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Robin J. Deeley, Rufus Willett. 2024-02-09. The rational HK-conjecture: transformation groupoids and a revised version. https://arxiv.org/abs/2402.06837

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