A Morse A-infinity model for the higher-dimensional Heegaard Floer homology of cotangent fibers

Given a smooth closed n-manifold M and a k-tuple of basepoints in M, we define a Morse-type A∞-algebra called the based multiloop A∞-algebra and show the equivalence with the higher-dimensional Heegaard Floer A∞-algebra of k disjoint cotangent fibers of T*M.