Rational K3 Homotopy and the Largest Mathieu Group

2025/09/23 by Carta, Federico, Duncan, John F. R., He, Yang-Hui
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2509.18969

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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• Tracking the symmetries of \mathbb Z₃-orbifold K3s within the Mathieu groups