Equivalence and slice theory for symplectic forms on closed manifolds

Swanson, R. C.; Chicone, C. C.

doi:10.1090/S0002-9939-1979-0516476-4

Equivalence and slice theory for symplectic forms on closed manifolds
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by R. C. Swanson and C. C. Chicone

Proc. Amer. Math. Soc. 73 (1979), 265-270

DOI: https://doi.org/10.1090/S0002-9939-1979-0516476-4

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Abstract:

In this paper, a study is made of the pullback action of the diffeomorphism group on the totality of symplectic forms on a compact manifold. For this action, the orbit is shown to be a smooth (Banach) manifold consisting of a denumerable union of submanifolds, each lying in a fixed cohomology class. In addition, a precise characterization is given of those symplectic manifolds for which there is a local factorization of the pullback action in the sense of a transverse “slice” of closed 2-forms, invariant under the group of symplectic diffeomorphisms.

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