%0 Journal Article
%T From Calabi-Yau dg Categories to Frobenius manifolds via Primitive Forms
%A Atsushi Takahashi
%J Mathematics
%D 2015
%I arXiv
%X 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.
%U http://arxiv.org/abs/1503.09099v2