Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants

Abstract

We prove that genus-zero and genus-one stationary Gromov–Witten invariants of ℙ1 arise as the Eynard–Orantin invariants of the spectral curve x = z + 1∕ z, y = ln z. As an application we show that tautological intersection numbers on the moduli space of curves arise in the asymptotics of large-degree Gromov–Witten invariants of ℙ1.