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arXiv · 0801.3446

A Characteristic Map for Symplectic Manifolds

Jerry Lodder
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Abstract

We construct a local characteristic map to a symplectic manifold M via certain cohomology groups of Hamiltonian vector fields. For each p in M, the Leibniz cohomology of the Hamiltonian vector fields on R^{2n} maps to the Leibniz cohomology of all Hamiltonian vector fields on M. For a particular extension g_n of the symplectic Lie algebra, the Leibniz cohomology of g_n is shown to be an exterior algebra on the canonical symplectic two-form. The Leibniz homology of g_n then maps to the Leibniz homology of Hamiltonian vector fields on R^{2n}.

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Jerry Lodder. 2008-01-22. A Characteristic Map for Symplectic Manifolds. https://arxiv.org/abs/0801.3446

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