2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138774We introduce a strong homotopy notion of a cyclic symmetric inner product of an A-infinity 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 non-constant symplectic structure on the corresponding formal non-commutative supermanifold. We show that (open Gromov-Witten type) potential for a cyclic filtered A-infinity algebra is invariant under the cyclic filtered A-infinity homomorphism up to reparametrization, cyclization and a constant addition, generalizing the work of Kajiura.25 pagesAlgebraic TopologySymplectic Geometry46CXX, 53DXXtext