Hamiltonian structures on foliations

Details Hamiltonian structures on foliations Hamiltonian structures on foliations

2002-02-04

arxiv.org/abs/math/0202021v1

Mathematics

Symplectic Geometry

LaTex, 18 pages

Scientific paper

We discuss hamiltonian structures of the Gelfand-Dorfman complex of projectable vector fields and differential forms on a foliated manifold. Such a structure defines a Poisson structure on the algebra of foliated functions, and embeds the given foliation into a larger, generalized foliation with presymplectic leaves. In a so-called tame case, the structure is induced by a Poisson structure of the manifold. Cohomology spaces and classes relevant to geometric quantization are also considered.

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