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arXiv · 1703.08279

On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies

Andrzej Czarnecki
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Abstract

We present a construction (and classification) of certain invariant 2-forms on the real symplectic group. They are used to define a symplectic form on the quotient by a maximal torus and to "lift" a symplectic structure from a symplectic manifold to the bundle of frames. This is a by-product of a failed attempt to prove certain finiteness theorems for basic symplectic cohomologies. In the last part of the paper we include a valid proof.

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Andrzej Czarnecki. 2017-03-24. On the Symplectic Structures in Frame Bundles and the Finite Dimension of Basic Symplectic Cohomologies. https://doi.org/10.3842/sigma.2018.029

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