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Equivalence and slice theory for symplectic forms on closed manifolds


Authors: R. C. Swanson and C. C. Chicone
Journal: Proc. Amer. Math. Soc. 73 (1979), 265-270
MSC: Primary 58D05; Secondary 58A10, 58D17
DOI: https://doi.org/10.1090/S0002-9939-1979-0516476-4
MathSciNet review: 516476
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0516476-4
Keywords: Symplectic forms, pullback, slice
Article copyright: © Copyright 1979 American Mathematical Society

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