Pixton's double ramification cycle relations

Abstract

We prove a conjecture of Pixton, namely that his proposed formula for the double ramification cycle on ${\bar{M}}_{g,n}$ vanishes in codimension beyond $g$. This yields a collection of tautological relations in the Chow ring of ${\bar{M}}_{g,n}$. We describe, furthermore, how these relations can be obtained from Pixton’s $3$–spin relations via localization on the moduli space of stable maps to an orbifold projective line.