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 1 arise as the Eynard–Orantin invariants of the spectral curve x = z + 1z, 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 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