On quasi-isomorphic DGBV algebras

Abstract.

 One of the methods to obtain Frobenius manifold structures is via differential Gerstenhaber-Batalin-Vilkovisky (DGBV) algebra construction. An important problem, as motivated from mirror symmetry, is how to identify Frobenius manifold structures constructed from two different DGBV algebras. For DGBV algebras with suitable conditions, we show the functorial property of a construction of deformations of the multiplicative structures of their cohomology. In particular, we show that quasi-isomorphic DGBV algebras yield equivalent formal Frobenius manifold structures.