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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.00182 |
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| _version_ | 1866909610721411072 |
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| author | Benameur, Moulay-Tahar Moulard, Victor |
| author_facet | Benameur, Moulay-Tahar Moulard, Victor |
| contents | Given a finitely generated discrete group Γ, we construct for any admissible crossed product completion and for any metrizable finite dimensional compact Γ-space X, a universal Higson-Roe six-term exact sequence for the transformation groupoid X\rtimes Γ. In particular, we generalize the maximal Higson- Roe sequence to such groupoids. In the case where the groupoid X\rtimes Γ satisfies the rectified Baum-Connes conjecture, this yields some rigidity consequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00182 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Admissible Higson-Roe sequences for transformation groupoids Benameur, Moulay-Tahar Moulard, Victor Operator Algebras 53C12, 57R30, 53C27, 32Q10, 19K33, 19K35, 19K56, 58B34 Given a finitely generated discrete group Γ, we construct for any admissible crossed product completion and for any metrizable finite dimensional compact Γ-space X, a universal Higson-Roe six-term exact sequence for the transformation groupoid X\rtimes Γ. In particular, we generalize the maximal Higson- Roe sequence to such groupoids. In the case where the groupoid X\rtimes Γ satisfies the rectified Baum-Connes conjecture, this yields some rigidity consequences. |
| title | Admissible Higson-Roe sequences for transformation groupoids |
| topic | Operator Algebras 53C12, 57R30, 53C27, 32Q10, 19K33, 19K35, 19K56, 58B34 |
| url | https://arxiv.org/abs/2411.00182 |