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On the Euler characteristic of the commutative graph complex and the top weight cohomology of $\mathcal M_g$
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abstract
We prove an asymptotic formula for the Euler characteristic of Kontsevich's commutative graph complex. This formula implies that the total amount of commutative graph homology grows super-exponentially with the rank and, via a theorem of Chan, Galatius, and Payne, that the dimension of the top weight cohomology of the moduli space of curves, $\mathcal M_g$, grows super-exponentially with the genus $g$.
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The 11-loop graph cohomology
The 11-loop Kontsevich graph cohomology is computed, and the vanishing [σ3, X10] = 0 is shown, providing a counterexample to a strong form of Brown's conjecture.
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