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On foliated, Poisson and Hamiltonian diffeomorphisms. (English) Zbl 0988.22010

The author studies some nontransitive groups of diffeomorphisms on smooth manifolds, showing that they can admit a Lie group structure. These groups are the leaf preserving diffeomorphism group of a foliated manifold and the group of Poisson and Hamiltonian diffeomorphisms of a regular Poisson manifold. The author uses some techniques presented in the book by A. Kriegl and P. W. Michor [The convenient setting of global analysis, Math. Surveys and Monographs, Providence (1997; Zbl 0889.58001)] in the case of the foliated picture. The “Poisson” flux homomorphism, which is strongly related to the Weinstein chart, enables one to give some characterizations of Hamiltonian diffeomorphisms and isotopies.

MSC:

22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
53D17 Poisson manifolds; Poisson groupoids and algebroids
57R50 Differential topological aspects of diffeomorphisms
57R30 Foliations in differential topology; geometric theory

Citations:

Zbl 0889.58001
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References:

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