Displaying similar documents to “4-dimensional c-symplectic S 1 -manifolds with non-empty fixed point set need not be c-Hamiltonian”

Induced differential forms on manifolds of functions

Cornelia Vizman (2011)

Archivum Mathematicum

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Differential forms on the Fréchet manifold ℱ ( S , M ) of smooth functions on a compact k -dimensional manifold S can be obtained in a natural way from pairs of differential forms on M and S by the hat pairing. Special cases are the transgression map Ω p ( M ) → Ω p - k ( ℱ ( S , M ) ) (hat pairing with a constant function) and the bar map Ω p ( M ) → Ω p ( ℱ ( S , M ) ) (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].

Toric structures on near-symplectic 4-manifolds

David T. Gay, Margaret Symington (2009)

Journal of the European Mathematical Society

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A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on...