By computing the LS12 and S16 motivic structures via graph complexes, the authors prove new nonvanishing middle cohomology for M9 and M11 and establish exponential growth of H_c^{2g+k}(M_g) for 21 previously unknown values of k.
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The motivic structures $\mathsf{LS}_{12}$ and $\mathsf{S}_{16}$ in the cohomology of moduli spaces of curves
By computing the LS12 and S16 motivic structures via graph complexes, the authors prove new nonvanishing middle cohomology for M9 and M11 and establish exponential growth of H_c^{2g+k}(M_g) for 21 previously unknown values of k.