#### Volume 18, issue 4 (2014)

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Gromov–Witten invariants of $\mathbb{P}^1$ and Eynard–Orantin invariants

### Paul Norbury and Nick Scott

Geometry & Topology 18 (2014) 1865–1910
##### Abstract

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 $x=z+1∕z$, $y=lnz$. 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 ${ℙ}^{1}$.

##### Keywords
Gromov–Witten, moduli space, Eynard–Orantin
Primary: 05A15
Secondary: 14N35