#### Volume 21, issue 4 (2017)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
The Eynard–Orantin recursion and equivariant mirror symmetry for the projective line

### Bohan Fang, Chiu-Chu Melissa Liu and Zhengyu Zong

Geometry & Topology 21 (2017) 2049–2092
##### Abstract

We study the equivariantly perturbed mirror Landau–Ginzburg model of ${ℙ}^{1}$. We show that the Eynard–Orantin recursion on this model encodes all-genus, all-descendants equivariant Gromov–Witten invariants of ${ℙ}^{1}$. The nonequivariant limit of this result is the Norbury–Scott conjecture, while by taking large radius limit we recover the Bouchard–Mariño conjecture on simple Hurwitz numbers.

##### Keywords
Gromov–Witten invariants, mirror symmetry, Eynard–Orantin recursion, Norbury–Scott conjecture
Primary: 14N35