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Compatible poisson structures on fibered 5-manifolds

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Abstract

We study a class of Poisson tensors on a fibered manifold which are compatible with the fiber bundle structure by the so-called almost coupling condition. In the case of a 5-dimensional orientable fibered manifolds with 2-dimensional bases, we describe a global behavior of almost coupling Poisson tensors and their singularities by using a bigraded factorization of the Jacobi identity. In particular, we present some unimodularity criteria and describe a class of gauge type transformations preserving the almost coupling property.

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Acknowledgements

This work was partially supported by the Mexican National Council of Science and Technology (CONACyT), under research project CB-2013-219631.

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Correspondence to J. C. Ruíz-Pantaleón.

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Flores-Espinoza, R., Ruíz-Pantaleón, J.C. & Vorobiev, Y. Compatible poisson structures on fibered 5-manifolds. Bol. Soc. Mat. Mex. 26, 187–209 (2020). https://doi.org/10.1007/s40590-018-0225-7

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Keywords

  • Poisson structures
  • Fiber bundles
  • Almost coupling tensors
  • Poisson connections

Mathematics Subject Classification

  • 53D17
  • 53C12
  • 70G45