Topological Mathieu Moonshine
Theo Johnson-Freyd

TL;DR
This paper investigates the $tmf$-cohomology of the classifying space of the Mathieu group $M_{24}$, providing detailed computations and conjectures related to Mathieu Moonshine and supersymmetric quantum field theories.
Contribution
It offers new computational results on $tmf$-cohomology of $BM_{24}$ and proposes a conjecture linking these results to Mathieu Moonshine and quantum field theory.
Findings
$tmf^{-27}_ ext{omega}(BM_{24})[rac12] = 0$ for nonzero $ ext{omega}$
Restriction map $tmf^{-3}_ ext{omega}(BM_{24})[rac12]$ is surjective for certain $ ext{omega}$
Supports conjecture about $Co_1$-twisted-equivariant $TMF$ and Mathieu Moonshine
Abstract
We explore the Atiyah-Hirzebruch spectral sequence for the -cohomology of the classifying space of the largest Mathieu group , twisted by a class . Our exploration includes detailed computations of the -cohomology of and of the first few differentials in the AHSS. We are specifically interested in the value of in cohomological degree . Our main computational result is that when . For comparison, the restriction map is surjective for one of the two nonzero values of . Our motivation comes from Mathieu Moonshine. Assuming a well-studied conjectural relationship between and supersymmetric quantum field…
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models
