Topological Recursion Relations from Pixton’s Formula

Abstract

We prove that every degree-g polynomial in the ψ-classes on ${\bar{\mathcal{M}}}_{\mathit{g},\mathit{n}}$ can be expressed as a sum of tautological classes supported on the boundary with no κ-classes. Such equations, which we refer to as topological recursion relations, can be used to deduce universal equations for the Gromov–Witten invariants of any target.