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The motivic structures $\mathsf{LS}_{12}$ and $\mathsf{S}_{16}$ in the cohomology of moduli spaces of curves

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arxiv 2411.12652 v1 pith:JEHLOW3X submitted 2024-11-19 math.AG

Samir Canning , Hannah Larson , Sam Payne , Thomas Willwacher This is my paper · ORCID
classification math.AG
keywords mathsfcohomologymathcalcurvesmodulispacesalmostappearances
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abstract

We study the appearances of $\mathsf{LS}_{12}$ and $\mathsf{S}_{16}$ in the weight-graded compactly supported cohomology of moduli spaces of curves. As applications, we prove new nonvanishing results for the middle cohomology groups of $\mathcal{M}_9$ and $\mathcal{M}_{11}$ and give evidence to support the conjecture that the dimension fo $H^{2g + k}_c(\mathcal{M}_g)$ grows at least exponentially with $g$ for almost all $k$.

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  1. Getzler-Kapranov graph complex cohomology computations in weight 13

    math.AG 2025-07 conditional novelty 5.0 of 10

    The weight-13 cohomology of M_{g,n} for 3g+2n=28 is computed via the Getzler-Kapranov graph complex, with explicit Sn-representations in two degrees.

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