Poisson Structures on Smooth 4–Manifolds

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

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)1533-1550
Number of pages18
JournalLetters in Mathematical Physics
Volume105
Issue number11
DOIs
StatePublished - Nov 1 2015

Fingerprint

Poisson Structure
Singularity
4-manifold
Homotopy
Vanish
Siméon Denis Poisson
Circle
Closed
Class
Form

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

García-Naranjo, L. C., Suárez-Serrato, P., & Vera, R. (2015). Poisson Structures on Smooth 4–Manifolds. Letters in Mathematical Physics, 105(11), 1533-1550. https://doi.org/10.1007/s11005-015-0792-8
García-Naranjo, Luis C. ; Suárez-Serrato, Pablo ; Vera, Ramón. / Poisson Structures on Smooth 4–Manifolds. In: Letters in Mathematical Physics. 2015 ; Vol. 105, No. 11. pp. 1533-1550.
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García-Naranjo, LC, Suárez-Serrato, P & Vera, R 2015, 'Poisson Structures on Smooth 4–Manifolds', Letters in Mathematical Physics, vol. 105, no. 11, pp. 1533-1550. https://doi.org/10.1007/s11005-015-0792-8

Poisson Structures on Smooth 4–Manifolds. / García-Naranjo, Luis C.; Suárez-Serrato, Pablo; Vera, Ramón.

In: Letters in Mathematical Physics, Vol. 105, No. 11, 01.11.2015, p. 1533-1550.

Research output: Contribution to journalArticle

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García-Naranjo LC, Suárez-Serrato P, Vera R. Poisson Structures on Smooth 4–Manifolds. Letters in Mathematical Physics. 2015 Nov 1;105(11):1533-1550. https://doi.org/10.1007/s11005-015-0792-8