Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 029, 12 pages      arXiv:1703.08279

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

Andrzej Czarnecki
Jagiellonian University, Łojasiewicza 6, 30-348 Krakow, Poland

Received February 16, 2018, in final form March 24, 2018; Published online March 30, 2018

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.

Key words: symplectic cohomology; basic cohomology.

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