English

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

K-Theory and Homology 2024-02-13 v1 Operator Algebras

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.

Keywords

Cite

@article{arxiv.2402.06837,
  title  = {The rational HK-conjecture: transformation groupoids and a revised version},
  author = {Robin J. Deeley and Rufus Willett},
  journal= {arXiv preprint arXiv:2402.06837},
  year   = {2024}
}

Comments

43 pages

R2 v1 2026-06-28T14:44:43.520Z