Isomorphisms in K-theory from isomorphisms in groupoid homology theories
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929534718181376 |
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| author | Miller, Alistair |
| author_facet | Miller, Alistair |
| contents | We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid homology induced by an étale correspondence yields an isomorphism in the K-theory of the associated $\mathrm{C}^\ast$-algebras. We apply this to extend X. Li's K-theory formula for left regular inverse semigroup $\mathrm{C}^\ast$-algebras. These results are obtained by developing the functoriality of the ABC spectral sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isomorphisms in K-theory from isomorphisms in groupoid homology theories Miller, Alistair K-Theory and Homology Operator Algebras 46L80, 20J05, 19K35, 18G80 We prove that for torsion-free amenable ample groupoids, an isomorphism in groupoid homology induced by an étale correspondence yields an isomorphism in the K-theory of the associated $\mathrm{C}^\ast$-algebras. We apply this to extend X. Li's K-theory formula for left regular inverse semigroup $\mathrm{C}^\ast$-algebras. These results are obtained by developing the functoriality of the ABC spectral sequence. |
| title | Isomorphisms in K-theory from isomorphisms in groupoid homology theories |
| topic | K-Theory and Homology Operator Algebras 46L80, 20J05, 19K35, 18G80 |
| url | https://arxiv.org/abs/2401.17240 |