Annals of Global Analysis and Geometry

, Volume 55, Issue 4, pp 777–804 | Cite as

Poisson and near-symplectic structures on generalized wrinkled fibrations in dimension 6

  • P. Suárez-Serrato
  • J. Torres OrozcoEmail author
  • R. Vera


We show that generalized broken fibrations in arbitrary dimensions admit rank-2 Poisson structures compatible with the fibration structure. After extending the notion of wrinkled fibration to dimension 6, we prove that these wrinkled fibrations also admit compatible rank-2 Poisson structures. In the cases with indefinite singularities, we can provide these wrinkled fibrations in dimension 6 with near-symplectic structures.


Singular Poisson Near-symplectic Broken Lefschetz fibrations Wrinkled Singularity theory Stable maps Fold Cusp Swallowtail Butterfly 

Mathematics Subject Classification

MSC 57R17 MSC 53D17 



We warmly thank Yankı Lekili for answering detailed questions about his paper. His explanations allowed us to complete our computations for the near-symplectic forms. We also thank Alan Weinstein for commenting on an early version of this paper. PSS thanks DGAPA PAPIIT-UNAM IN102716 and The University of California Institute for Mexico and the United States (UC MEXUS) Grant CN-16-43, the organizers of the meeting ’Gone fishing 2016’ in Boulder, and IPAM in UCLA where some of this work was done. RV thanks UNAM-DGAPA and the partial support by the FWO under EOS project G0H4518N. JTO thanks support from CONACyT Project CB2016/283960.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMexico CityMexico
  2. 2.Department of MathematicsUniversity of California Santa BarbaraGoletaUSA
  3. 3.Centro de Ciencias MatemáticasUniversidad Nacional Autónoma de MéxicoMoreliaMexico
  4. 4.Department of MathematicsKU LeuvenLeuven (Heverlee)Belgium

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