From Calabi-Yau dg Categories to Frobenius manifolds via Primitive Forms

Atsushi Takahashi

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arXiv · 1503.09099

From Calabi-Yau dg Categories to Frobenius manifolds via Primitive Forms

Atsushi Takahashi

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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. Under an assumption on the formality of a certain homotopy algebra, a formal primitive form for a smooth compact Calabi-Yau dg algebra can be constructed, which enable us to have a formal Frobenius manifold.

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Atsushi Takahashi. 2015-03-31. From Calabi-Yau dg Categories to Frobenius manifolds via Primitive Forms. https://arxiv.org/abs/1503.09099

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