The rational HK-conjecture: transformation groupoids and a revised version
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| Format: | Preprint |
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2024
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| _version_ | 1866914673909039104 |
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| author | Deeley, Robin J. Willett, Rufus |
| author_facet | Deeley, Robin J. Willett, Rufus |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_06837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The rational HK-conjecture: transformation groupoids and a revised version Deeley, Robin J. Willett, Rufus K-Theory and Homology Operator Algebras 46L80, 22A22 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. |
| title | The rational HK-conjecture: transformation groupoids and a revised version |
| topic | K-Theory and Homology Operator Algebras 46L80, 22A22 |
| url | https://arxiv.org/abs/2402.06837 |