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VOL. 83 | 2019 From a class of Calabi–Yau dg algebras to Frobenius manifolds via primitive forms
Atsushi Takahashi

Editor(s) Kentaro Hori, Changzheng Li, Si Li, Kyoji Saito

Abstract

It is one of the most important problems in mirror symmetry to obtain functorially Frobenius manifolds from smooth compact Calabi–Yau $A_\infty$-categories. This paper gives an approach to this problem based on the theory of primitive forms and, in particular, reduces it to a formality conjecture of certain homotopy algebra. Under this formality conjecture, a formal primitive form for a non-negatively graded connected smooth compact Calabi–Yau dg algebra can be constructed, which enable us to have a formal Frobenius manifold.

Information

Published: 1 January 2019
First available in Project Euclid: 26 December 2019

zbMATH: 07276149

Digital Object Identifier: 10.2969/aspm/08310389

Subjects:
Primary: 14J33, 53D37, 53D45

Rights: Copyright © 2019 Mathematical Society of Japan

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