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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On the remodeling conjecture for toric Calabi-Yau 3-orbifolds
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by Bohan Fang, Chiu-Chu Melissa Liu and Zhengyu Zong HTML | PDF
J. Amer. Math. Soc. 33 (2020), 135-222 Request permission

Abstract:

The Remodeling Conjecture proposed by Bouchard-Klemm-Mariño-Pasquetti (BKMP) relates the A-model open and closed topological string amplitudes (the all genus open and closed Gromov-Witten invariants) of a semiprojective toric Calabi-Yau 3-manifold/3-orbifold to the Eynard-Orantin invariants of its mirror curve. It is an all genus open-closed mirror symmetry for toric Calabi-Yau 3-manifolds/3-orbifolds. In this paper, we present a proof of the BKMP Remodeling Conjecture for all genus open-closed orbifold Gromov-Witten invariants of an arbitrary semiprojective toric Calabi-Yau 3-orbifold relative to an outer framed Aganagic-Vafa Lagrangian brane. We also prove the conjecture in the closed string sector at all genera.
References
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Additional Information
  • Bohan Fang
  • Affiliation: Beijing International Center for Mathematical Research, Peking University, 5 Yiheyuan Road, Beijing 100871, People’s Republic of China
  • MR Author ID: 831818
  • Email: bohanfang@gmail.com
  • Chiu-Chu Melissa Liu
  • Affiliation: Department of Mathematics, Columbia University, 2990 Broadway, New York, New York 10027
  • MR Author ID: 691648
  • Email: ccliu@math.columbia.edu
  • Zhengyu Zong
  • Affiliation: Yau Mathematical Sciences Center, Tsinghua University, Jin Chun Yuan West Building, Tsinghua University, Haidian District, Beijing 100084, People’s Republic of China
  • MR Author ID: 1056175
  • Email: zyzong@mail.tsinghua.edu.cn
  • Received by editor(s): March 31, 2018
  • Received by editor(s) in revised form: June 20, 2019
  • Published electronically: November 1, 2019
  • Additional Notes: The first author was partially supported by a start-up grant at Peking University
    The second author was partially supported by NSF grants DMS-1206667 and DMS-1159416
    The third author was partially supported by the start-up grant at Tsinghua University
  • © Copyright 2019 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 33 (2020), 135-222
  • MSC (2010): Primary 14N35, 15D35, 14J33
  • DOI: https://doi.org/10.1090/jams/934
  • MathSciNet review: 4066474