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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29985 |
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| _version_ | 1866918420819214336 |
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| author | Faurot, Gregory Ferrer, Giovanni |
| author_facet | Faurot, Gregory Ferrer, Giovanni |
| contents | We compute the homotopy groups at each unital abelian C*-algebra $C(T)$ in the Morita $3$-category of abelian C*-algebras, C*-algebras with central maps, C*-correspondences, and adjointable bimodule maps. We describe these groups in terms of the topological data of the underlying compact Hausdorff space $T$. We also compute the actions of the first homotopy group on the second and third homotopy groups in terms of these topological invariants of $T$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29985 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Homotopy 3-Type of Abelian C*-Algebras Faurot, Gregory Ferrer, Giovanni Operator Algebras Category Theory Quantum Algebra 46M15, 18N20, 46L05 We compute the homotopy groups at each unital abelian C*-algebra $C(T)$ in the Morita $3$-category of abelian C*-algebras, C*-algebras with central maps, C*-correspondences, and adjointable bimodule maps. We describe these groups in terms of the topological data of the underlying compact Hausdorff space $T$. We also compute the actions of the first homotopy group on the second and third homotopy groups in terms of these topological invariants of $T$. |
| title | The Homotopy 3-Type of Abelian C*-Algebras |
| topic | Operator Algebras Category Theory Quantum Algebra 46M15, 18N20, 46L05 |
| url | https://arxiv.org/abs/2603.29985 |