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Poisson structures on wrinkled fibrations

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Abstract

We provide local formulae for Poisson bivectors and symplectic forms on the leaves of Poisson structures associated with wrinkled fibrations on smooth 4-manifolds. When such a fibration structure does not have 2-spheres in its fibres, the associated Poisson structure is integrable.

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Acknowledgments

We thank Gerardo Sosa for allowing us to use the figures in this paper, which originally appeared in [10], and Luis García-Naranjo for commenting on an earlier version. We thank the referees for suggesting how to simplify the computations, and for pointing out the relationships with integrability and linearization. PSS thanks CIMAT in Guanajuato for its warm hospitality in visits where this work was produced, and CONACyT-México for supporting various research activities.

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Authors and Affiliations

  1. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, Coyoacán, 04510, Mexico City, Mexico

    P. Suárez-Serrato

  2. CIMAT, Jalisco S/N, Valenciana, Guanajuato, Mexico

    J. Torres Orozco

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  1. P. Suárez-Serrato
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  2. J. Torres Orozco
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Correspondence to P. Suárez-Serrato.

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Suárez-Serrato, P., Torres Orozco, J. Poisson structures on wrinkled fibrations. Bol. Soc. Mat. Mex. 22, 263–280 (2016). https://doi.org/10.1007/s40590-015-0072-8

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  • DOI: https://doi.org/10.1007/s40590-015-0072-8

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