## Geometry & Topology

### Gromov–Witten invariants of $\mathbb{P}^1$ 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 $x=z+1∕z$, $y= lnz$. 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 $ℙ1$.

#### Article information

Source
Geom. Topol., Volume 18, Number 4 (2014), 1865-1910.

Dates
Revised: 6 December 2013
Accepted: 27 February 2014
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732855

Digital Object Identifier
doi:10.2140/gt.2014.18.1865

Mathematical Reviews number (MathSciNet)
MR3268770

Zentralblatt MATH identifier
1308.05011

#### Citation

Norbury, Paul; Scott, Nick. Gromov–Witten invariants of $\mathbb{P}^1$ and Eynard–Orantin invariants. Geom. Topol. 18 (2014), no. 4, 1865--1910. doi:10.2140/gt.2014.18.1865. https://projecteuclid.org/euclid.gt/1513732855

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