Strong homotopy inner product of an A∞-algebra.

We introduce a strong homotopy notion of a cyclic symmetric inner product of an A∞-algebra and prove a characterization theorem in the formalism of the infinity inner products by Tradler. We also show that it is equivalent to the notion of a nonconstant symplectic structure on the corresponding formal noncommutative supermanifold. We show that (open Gromov–Witten type) potential for a cyclic filtered A∞-algebra is invariant under the cyclic filtered A∞-homomorphism up to reparameterization, cyclization, and a constant addition, generalizing the work of Kajiura. [ABSTRACT FROM PUBLISHER]