Poisson cohomology of broken Lefschetz fibrations

Batakidis, Panagiotis; Vera, Ramón

doi:10.1016/j.difgeo.2020.101661

Differential Geometry and its Applications

2020

DOI: 10.1016/j.difgeo.2020.101661

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Poisson cohomology of broken Lefschetz fibrations

Panagiotis Batakidis

Ramón Vera

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2021

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Poisson structures of near-symplectic manifolds and their cohomology

Batakidis

Vera

2021

Journal of Mathematical Physics

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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 neighborhood of the singular locus Zω of the 2-form ω; it is of maximal rank 4, and it vanishes on a degeneracy set containing Zω. 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 with a near-symplectic 4-manifold.

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Poisson structures of near-symplectic manifolds and their cohomology

Batakidis

Vera

2021

Journal of Mathematical Physics

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Poisson cohomology of broken Lefschetz fibrations

Cited by 1 publication

References 13 publications

Poisson structures of near-symplectic manifolds and their cohomology

Poisson structures of near-symplectic manifolds and their cohomology

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