Poisson Structures on Smooth 4–Manifolds

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

doi:10.1007/s11005-015-0792-8

Poisson Structures on Smooth 4–Manifolds

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

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1533-1550
Number of pages	18
Journal	Letters in Mathematical Physics
Volume	105
Issue number	11
DOIs	https://doi.org/10.1007/s11005-015-0792-8
State	Published - Nov 1 2015

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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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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