Rational K3 Homotopy and the Largest Mathieu Group
Representation Theory
2025-09-24 v1 High Energy Physics - Theory
Algebraic Geometry
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.
Cite
@article{arxiv.2509.18969,
title = {Rational K3 Homotopy and the Largest Mathieu Group},
author = {Federico Carta and John F. R. Duncan and Yang-Hui He},
journal= {arXiv preprint arXiv:2509.18969},
year = {2025}
}
Comments
32 pages