Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants

Norbury, Paul¹ ; Scott, Nick²

¹ Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
² Mathematics and Statistics, University of Melbourne, Melbourne 3010, Australia

Geometry & topology, Tome 18 (2014) no. 4, pp. 1865-1910.

Résumé

We prove that genus-zero and genus-one stationary Gromov–Witten invariants of ${\mathbb{P}}^1$ 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 ${\mathbb{P}}^1$.

Détail

DOI : 10.2140/gt.2014.18.1865

Classification : 05A15, 14N35
Keywords: Gromov–Witten, moduli space, Eynard–Orantin

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