THE MASLOV COCYCLE, SMOOTH STRUCTURES, AND REAL-ANALYTIC COMPLETE INTEGRABILITY.

This paper proves two main results. First, it is shown that if Σ is a smooth manifold homeomorphic to the standard n-torus Tⁿ = Rⁿ/Zⁿ and H is a real-analytically completely integrable convex hamiltonian on T*Σ, then Σ is diffeomorphic to Tⁿ. Second, it is proven that for some topological 7-manifolds, the cotangent bundle of each smooth structure admits a real-analytically completely integrable riemannian metric hamiltonian. [ABSTRACT FROM AUTHOR]