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arXiv · 2605.04950

A low-valence ribbon graph complex computing the cohomology of $M_{g,m}$

Sergei A. Merkulov
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Abstract

It is proven that every cohomology class of the moduli space $M_{g,m}$ for any $2g+m\geq 3$, $m\geq 1$ can be represented combinatorially by a ribbon quiver with at most four-valent vertices. The "at most four"-valency condition is sharp.

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Sergei A. Merkulov. 2026-05-06. A low-valence ribbon graph complex computing the cohomology of $M_{g,m}$. https://arxiv.org/abs/2605.04950

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