The Kunneth theorem for the Fukaya algebra of a product of Lagrangians

Given a compact Lagrangian submanifold L of a symplectic manifold (M , omega), Fukaya, Oh, Ohta and Ono construct a filtered A(infinity)-algebra F(L), on the cohomology of L, which we call the Fukaya algebra of L. In this paper, we describe the Fukaya algebra of a product of two Lagrangians submanifolds L-1 x L-2. Namely, we show that F(L-1 x L-2) is quasi-isomorphic to F(L-1) circle times(infinity) F(L-2), where circle times(infinity) is the tensor product of filtered A(infinity)-algebras defined in [L. Amorim, Tensor product of filtered A(infinity)-algebras, J. Pure Appl. Algebra 220(12) (2016) 3984-4016]. As a corollary of this quasi-isomorphism, we obtain a description of the bounding cochains on F(L-1 x L-2) and of the Floer cohomology of L-1 x L-2.