Topological recursion relations from Pixton's formula

Abstract

We prove that every degree-g polynomial in the $\psi$-classes on ${\overline{\mathcal{M}}}_{g,n}$ can be expressed as a sum of tautological classes supported on the boundary with no $\kappa$-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.

v2: agrees with published version; 17 pages