### Examples of circle actions on symplectic spaces

Christopher Allday (1998)

Banach Center Publications

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Christopher Allday (1998)

Banach Center Publications

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John Oprea (1998)

Banach Center Publications

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Cornelia Vizman (2011)

Archivum Mathematicum

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

Goldberg, Timothy E. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Chris Woodward (2010)

Les cours du CIRM

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Chris Woodward (2010)

Les cours du CIRM

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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...