Volume 21, issue 4 (2017)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
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 1. We show that the Eynard–Orantin recursion on this model encodes all-genus, all-descendants equivariant Gromov–Witten invariants of 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
Mathematical Subject Classification 2010
Primary: 14N35
References
Publication
Received: 6 December 2014
Revised: 24 May 2016
Accepted: 16 July 2016
Published: 19 May 2017
Proposed: Lothar Göttsche
Seconded: Richard Thomas, Dan Abramovich
Authors
Bohan Fang
Beijing International Center for Mathematical Research
Peking University
5 Yiheyuan Road
Jingchunyuan 78
Beijing, 100871
China
Chiu-Chu Melissa Liu
Department of Mathematics
Columbia University
Room 623, Mail Code 4435
2990 Broadway
New York, NY 10027
United States
Zhengyu Zong
Yau Mathematical Sciences Center
Tsinghua University
Jing Chun Yuan West Building, Tsinghua University
Haidian District
Beijing, 100084
China