Recently, Tsai-Tseng-Yau constructed new invariants of symplectic manifolds:
a sequence of A-infinity algebras built of differential forms on the symplectic manifold.
We show that these symplectic A-infinity algebras have a simple topological interpretation.
Namely, when the cohomology class of the symplectic form is integral, these A-infinity algebras
are equivalent to the standard de Rham differential graded algebra on certain odd dimensional
sphere bundles over the symplectic manifold. From this equivalence, we
deduce for a closed symplectic manifold that Tsai-Tseng-Yau's symplectic A-infinity algebras
satisfy the Calabi-Yau property, and importantly, that they can be used to define an
intersection theory for coisotropic/isotropic chains. We further demonstrate that these
symplectic A-infinity algebras satisfy several functorial properties and lay the groundwork for
addressing Weinstein functoriality and invariance in the smooth category.