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.


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


Zbl 0889.58001
Full Text: DOI


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