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

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.

22 pages. This article is based on a talk given in Kavli IPMU at the workshop "Primitive forms and related subjects" on February 11th 2014. Corrected typos and minor errors

References in corpus (2)

• Calabi-Yau algebras
• Formality of the homotopy calculus algebra of Hochschild (co)chains