Lie graph homology model for [formula omitted

Abstract

This paper develops a new chain model for the commutative graph complex GC2 which takes Lie graph homology as an input. Our main technical result is the identification of a large contractible complex of (certain) tadpoles and higher genus vertices of the Feynman transform of Lie graph homology. Using this result we identify the anti-invariants of Lie graph homology in genus 2 with relations between bracketings of conjectural generators of grt1 in depth 2 modulo depth 3, unifying two a priori disparate appearances of the space of modular cusp forms in the study of graph homology.