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

Abstract

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

arXiv commentTwo new results are aded: Proposition 2.4.1 and Corollary 2.10. New version 19 pages