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

 Recent Issues
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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
##### Publication
Received: 18 July 2011
Revised: 6 December 2013
Accepted: 27 February 2014
Published: 2 October 2014
Proposed: Lothar Göttsche
Seconded: Jim Bryan, Yasha Eliashberg
##### Authors
 Paul Norbury Department of Mathematics and Statistics University of Melbourne Victoria 3010 Australia http://www.ms.unimelb.edu.au/~pnorbury Nick Scott Mathematics and Statistics University of Melbourne Melbourne 3010 Australia