4-dimensional c-symplectic $S^1$-manifolds with non-empty fixed point set need not be c-Hamiltonian

Akio Hattori

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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 $Ω^{p} (M) \to Ω^{p - k} (ℱ (S, M))$ (hat pairing with a constant function) and the bar map $Ω^{p} (M) \to Ω^{p} (ℱ (S, M))$ (hat pairing with a volume form). We develop a hat calculus similar to the tilda calculus for non-linear Grassmannians [6].

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Toric structures on near-symplectic 4-manifolds

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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...

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

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Toric structures on near-symplectic 4-manifolds

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