The Euler characteristic of the moduli space of graphs

Michael Borinsky; Karen Vogtmann

doi:10.1016/j.aim.2023.109290

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arXiv · 2301.01121

The Euler characteristic of the moduli space of graphs

Michael Borinsky·Karen Vogtmann

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Abstract

The moduli space of rank $n$ graphs, the outer automorphism group of the free group of rank $n$ and Kontsevich's Lie graph complex have the same rational cohomology. We show that the associated Euler characteristic grows like $-e^{-1/4}\,(n/e)^n/(n\log n)^2$ as $n$ goes to infinity, and thereby prove that the total dimension of this cohomology grows rapidly with $n$.

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BibTeX RIS

Michael Borinsky, Karen Vogtmann. 2023-01-03. The Euler characteristic of the moduli space of graphs. https://doi.org/10.1016/j.aim.2023.109290

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