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On the group of diffeomorphisms preserving a locally conformal symplectic structure. (English) Zbl 0940.53044

The concept of a locally conformal symplectic structure provides an interesting generalization of symplectic geometry, in particular since manifolds with such structures can serve as natural phase spaces of Hamiltonian dynamical systems. In the present paper, the authors study the automorphism group of a locally conformal symplectic structure. They prove that many properties of the symplectomorphism group studied by A. Banyaga [Comment. Math. Helv. 53, 174-227 (1978; Zbl 0393.58007)] have analogues for such an automorphism group. By using a special type of cohomology, the flux and Calabi homomorphisms are introduced. The main theorem states that the kernels of these homomorphisms are simple groups.

MSC:

53D05 Symplectic manifolds (general theory)
57R50 Differential topological aspects of diffeomorphisms

Citations:

Zbl 0393.58007
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