Geometry & Topology

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

Paul Norbury and Nick Scott

Full-text: Open access

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.

Article information

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

Dates
Received: 18 July 2011
Revised: 6 December 2013
Accepted: 27 February 2014
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]
Secondary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

Keywords
Gromov–Witten moduli space Eynard–Orantin

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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