Stirling decomposition of graph homology in genus 1

Abstract

We prove that commutative graph homology in genus g = 1 g=1 with n ≥ 3 n\geq 3 markings has a direct sum decomposition whose summands have rank given by Stirling numbers of the first kind. These summands are computed as the homology of complexes of certain decorated trees which have an elementary combinatorial description.