Abstract
We show that every closed oriented smooth 4-manifold admits a complete singular Poisson structure in each homotopy class of maps to the 2-sphere. The rank of this structure is 2 outside a small singularity set, which consists of finitely many circles and isolated points. The Poisson bivector vanishes on the singularities, where we give its local form explicitly.
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García-Naranjo, L.C., Suárez-Serrato, P. & Vera, R. Poisson Structures on Smooth 4–Manifolds. Lett Math Phys 105, 1533–1550 (2015). https://doi.org/10.1007/s11005-015-0792-8
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DOI: https://doi.org/10.1007/s11005-015-0792-8