On the Euler characteristic of the commutative graph complex and the top weight cohomology of $\mathcal M_g$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917751758520320 |
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| author | Borinsky, Michael Zagier, Don |
| author_facet | Borinsky, Michael Zagier, Don |
| contents | 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 $g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04190 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Euler characteristic of the commutative graph complex and the top weight cohomology of $\mathcal M_g$ Borinsky, Michael Zagier, Don Algebraic Topology Mathematical Physics Algebraic Geometry Combinatorics 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 $g$. |
| title | On the Euler characteristic of the commutative graph complex and the top weight cohomology of $\mathcal M_g$ |
| topic | Algebraic Topology Mathematical Physics Algebraic Geometry Combinatorics |
| url | https://arxiv.org/abs/2405.04190 |