Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants

Norbury, Paul; Scott, Nick

doi:10.2140/gt.2014.18.1865

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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

DOI: 10.2140/gt.2014.18.1865

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 $x = z + 1 ∕ z$ , $y = ln z$ . 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 $ℙ^{1}$ .

Keywords

Gromov–Witten, moduli space, Eynard–Orantin

Mathematical Subject Classification 2010

Primary: 05A15

Secondary: 14N35

References

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

Volume 18, issue 4 (2014)