This article is cited in 1 paper

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

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.

Keywords: symplectic cohomology; basic cohomology.

MSC: 53C12; 57R18

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

Language: English

DOI: 10.3842/SIGMA.2018.029

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