Gromov-Witten invariants of P~1 and Eynard-Orantin invariants

摘要

We prove that genus-zero and genus-one stationary Gromov-Witten invariants of P~1 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 P~1.