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arXiv · 2509.18969

Rational K3 Homotopy and the Largest Mathieu Group

Federico Carta·John F. R. Duncan·Yang-Hui He
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Abstract

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.

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Federico Carta, John F. R. Duncan, Yang-Hui He. 2025-09-23. Rational K3 Homotopy and the Largest Mathieu Group. https://arxiv.org/abs/2509.18969

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