A genus-4 topological recursion relation for Gromov-Witten invariants

Abstract

In this paper, we give a new genus-4 topological recursion relation for Gromov-Witten invariants of compact symplectic manifolds via Pixton's relations on the moduli space of curves. As an application, we prove Pixton's relations imply a known topological recursion relation on $\bar{\mathcal{M}}_{g,1}$ for genus $g\leq4$.