On Completely Integrable Systems with Local Torus Actions |
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Authors: | Mikhail Kogan |
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Institution: | (1) Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A |
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Abstract: | This paper concerns with symplectic topology of compact completely integrable Hamiltonian systems with only stable nondegenerate elliptic singularities. We describe all systems whose universal coverings admit actian-angle coordinates and, in particular, prove that some finite cover of a base space is diffeomorphic to a product of a convex polytope and a solvmanifold. We also construct an obstruction, vanishing of which guarantees splitting of some finite cover of a phase space as a toric variety and a torus fibering over a solvmanifold. |
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Keywords: | completely integrable systems Hamiltonian torus actions |
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