Poisson Structures on Smooth 4–Manifolds

Luis C. García-Naranjo, Pablo Suárez-Serrato, Ramón Vera

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1533-1550
Number of pages18
JournalLetters in Mathematical Physics
Issue number11
StatePublished - Nov 1 2015

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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