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

It is one of the most important problems in mirror symmetry to obtain functorially Frobenius manifolds from smooth compact Calabi-Yau $A_{\mathrm{\infty }}$-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.