Geometry & Topology Volume 21, issue 4 (2017)

Download this article
	For screen
	For printing

Recent Issues

The Journal

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

DOI: 10.2140/gt.2017.21.2049

Bibliography

1	G Borot, B Eynard, M Mulase, B Safnuk, A matrix model for simple Hurwitz numbers, and topological recursion, J. Geom. Phys. 61 (2011) 522 MR2746135
2	V Bouchard, M Mariño, Hurwitz numbers, matrix models and enumerative geometry, from: "From Hodge theory to integrability and TQFT tt∗–geometry" (editors R Y Donagi, K Wendland), Proc. Sympos. Pure Math. 78, Amer. Math. Soc. (2008) 263 MR2483754
3	B Dubrovin, Geometry of 2D topological field theories, from: "Integrable systems and quantum groups" (editors M Francaviglia, S Greco), Lecture Notes in Math. 1620, Springer (1996) 120 MR1397274
4	P Dunin-Barkowski, M Kazarian, N Orantin, S Shadrin, L Spitz, Polynomiality of Hurwitz numbers, Bouchard–Mariño conjecture, and a new proof of the ELSV formula, Adv. Math. 279 (2015) 67 MR3345179
5	P Dunin-Barkowski, N Orantin, S Shadrin, L Spitz, Identification of the Givental formula with the spectral curve topological recursion procedure, Comm. Math. Phys. 328 (2014) 669 MR3199996
6	T Ekedahl, S Lando, M Shapiro, A Vainshtein, Hurwitz numbers and intersections on moduli spaces of curves, Invent. Math. 146 (2001) 297 MR1864018
7	B Eynard, Intersection numbers of spectral curves, preprint (2011) arXiv:1104.0176
8	B Eynard, Invariants of spectral curves and intersection theory of moduli spaces of complex curves, Commun. Number Theory Phys. 8 (2014) 541 MR3282995
9	B Eynard, M Mulase, B Safnuk, The Laplace transform of the cut-and-join equation and the Bouchard–Mariño conjecture on Hurwitz numbers, Publ. Res. Inst. Math. Sci. 47 (2011) 629 MR2849645
10	B Eynard, N Orantin, Invariants of algebraic curves and topological expansion, Commun. Number Theory Phys. 1 (2007) 347 MR2346575
11	B Eynard, N Orantin, Computation of open Gromov–Witten invariants for toric Calabi–Yau 3–folds by topological recursion, a proof of the BKMP conjecture, Comm. Math. Phys. 337 (2015) 483 MR3339157
12	B Fang, Homological mirror symmetry is T–duality for ℙn, Commun. Number Theory Phys. 2 (2008) 719 MR2492197
13	B Fang, Central charges of T–dual branes for toric varieties, preprint (2016) arXiv:1611.05153
14	B Fang, C C M Liu, D Treumann, E Zaslow, T–duality and homological mirror symmetry for toric varieties, Adv. Math. 229 (2012) 1875 MR2871160
15	B Fang, C C M Liu, Z Zong, All genus open-closed mirror symmetry for affine toric Calabi–Yau 3–orbifolds, preprint (2013) arXiv:1310.4818
16	J D Fay, Theta functions on Riemann surfaces, 352, Springer (1973) MR0335789
17	A B Givental, Equivariant Gromov–Witten invariants, Internat. Math. Res. Notices 1996 (1996) 613 MR1408320
18	A Givental, Elliptic Gromov–Witten invariants and the generalized mirror conjecture, from: "Integrable systems and algebraic geometry" (editors M H Saito, Y Shimizu, K Ueno), World Sci. (1998) 107 MR1672116
19	A B Givental, Gromov–Witten invariants and quantization of quadratic Hamiltonians, Mosc. Math. J. 1 (2001) 551 MR1901075
20	A B Givental, Semisimple Frobenius structures at higher genus, Internat. Math. Res. Notices 2001 (2001) 1265 MR1866444
21	T Graber, R Vakil, Hodge integrals and Hurwitz numbers via virtual localization, Compositio Math. 135 (2003) 25 MR1955162
22	H Iritani, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math. 222 (2009) 1016 MR2553377
23	I Kostov, N Orantin, CFT and topological recursion, J. High Energy Phys. (2010) MR2795103
24	Y P Lee, R Pandharipande, Frobenius manifolds, Gromov–Witten theory, and Virasoro constraints, preprint (2004)
25	B H Lian, K Liu, S T Yau, Mirror principle, I, Asian J. Math. 1 (1997) 729 MR1621573
26	P Norbury, N Scott, Gromov–Witten invariants of ℙ1 and Eynard–Orantin invariants, Geom. Topol. 18 (2014) 1865 MR3268770
27	A Okounkov, R Pandharipande, Gromov–Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. 163 (2006) 517 MR2199225
28	A Okounkov, R Pandharipande, The equivariant Gromov–Witten theory of P1, Ann. of Math. 163 (2006) 561 MR2199226
29	J S Song, Y S Song, On a conjecture of Givental, J. Math. Phys. 45 (2004) 4539 MR2105206