  Any smooth, closed oriented 4-manifold has a surface diagram of arbitrarily
high genus g>2 that specifies it up to diffeomorphism. The goal of this paper
is to prove the following statement: For any smooth, closed oriented 4-manifold
M, there is a sequence of weak A-infinity algebras indexed by g, and the
homotopy equivalence class of each entry of this sequence is a diffeomorphism
invariant of M.
