On the Euler characteristic of the commutative graph complex and the top weight cohomology of $\mathcal M_g$

Michael Borinsky; Don Zagier

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arXiv · 2405.04190

On the Euler characteristic of the commutative graph complex and the top weight cohomology of $\mathcal M_g$

Michael Borinsky·Don Zagier

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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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Michael Borinsky, Don Zagier. 2024-05-07. On the Euler characteristic of the commutative graph complex and the top weight cohomology of $\mathcal M_g$. https://arxiv.org/abs/2405.04190

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