Contractible Cuntz classes in $Z$-stable C$^*$-algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909430829809664 |
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| author | Ouseph, Chrisil Toms, Andrew S. |
| author_facet | Ouseph, Chrisil Toms, Andrew S. |
| contents | Let $A$ be a unital, simple and Z-stable C$^*$-algebra. We show that the set of positive elements in $A$ (resp. $A \otimes K$) belonging to a fixed non-compact Cuntz class is contractible as a topological subspace of $A$ (resp. $A \otimes K$). In light of earlier work by Zhang, Jiang and Hua in the compact case, we deduce a complete calculation of the homotopy groups of Cuntz classes for these algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12366 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Contractible Cuntz classes in $Z$-stable C$^*$-algebras Ouseph, Chrisil Toms, Andrew S. Operator Algebras 46L05, 55Q52 Let $A$ be a unital, simple and Z-stable C$^*$-algebra. We show that the set of positive elements in $A$ (resp. $A \otimes K$) belonging to a fixed non-compact Cuntz class is contractible as a topological subspace of $A$ (resp. $A \otimes K$). In light of earlier work by Zhang, Jiang and Hua in the compact case, we deduce a complete calculation of the homotopy groups of Cuntz classes for these algebras. |
| title | Contractible Cuntz classes in $Z$-stable C$^*$-algebras |
| topic | Operator Algebras 46L05, 55Q52 |
| url | https://arxiv.org/abs/2412.12366 |