Rational K3 Homotopy and the Largest Mathieu Group
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909802376986624 |
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| author | Carta, Federico Duncan, John F. R. He, Yang-Hui |
| author_facet | Carta, Federico Duncan, John F. R. He, Yang-Hui |
| contents | We interpret the ranks of the rational homotopy groups of a K3 surface as dimensions of representations for the largest sporadic simple Mathieu group. We then construct a vertex algebra equipped with an action by the largest Mathieu group, and use it to associate Jacobi forms to this interpretation, in a compatible way. Our results suggest a topological role for the sporadic simple Mathieu groups in the theory of K3 surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18969 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rational K3 Homotopy and the Largest Mathieu Group Carta, Federico Duncan, John F. R. He, Yang-Hui Representation Theory High Energy Physics - Theory Algebraic Geometry We interpret the ranks of the rational homotopy groups of a K3 surface as dimensions of representations for the largest sporadic simple Mathieu group. We then construct a vertex algebra equipped with an action by the largest Mathieu group, and use it to associate Jacobi forms to this interpretation, in a compatible way. Our results suggest a topological role for the sporadic simple Mathieu groups in the theory of K3 surfaces. |
| title | Rational K3 Homotopy and the Largest Mathieu Group |
| topic | Representation Theory High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2509.18969 |