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

TL;DR

This paper introduces a new genus-4 topological recursion relation for Gromov-Witten invariants of symplectic manifolds, utilizing Pixton's relations, and demonstrates its implications for known recursion relations in moduli space.

Contribution

It presents a novel genus-4 recursion relation for Gromov-Witten invariants derived from Pixton's relations, expanding the theoretical framework.

Findings

Established a new genus-4 topological recursion relation

Proved Pixton's relations imply existing recursion relations for genus up to 4

Enhanced understanding of Gromov-Witten invariants in symplectic geometry

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 $g\leq4$.