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arXiv · 1702.03541

Poisson structures of near-symplectic manifolds and their cohomology

Panagiotis Batakidis·Ramón Vera
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Abstract

We connect Poisson and near-symplectic geometry by showing that there is a singular Poisson structure on a near-symplectic 4-manifold. The Poisson structure $π$ is defined on the tubular neighbourhood of the singular locus $Z_ω$ of the 2-form $ω$, it is of maximal rank 4 and it vanishes on a degeneracy set containing $Z_ω$. We compute its smooth Poisson cohomology, which depends on the modular vector field and it is finite dimensional. We conclude with a discussion on the relation between the Poisson structure $π$ and the overtwisted contact structure associated to a near-symplectic 4-manifold.

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Panagiotis Batakidis, Ramón Vera. 2021-03-26. Poisson structures of near-symplectic manifolds and their cohomology. https://doi.org/10.1063/5.0041230

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