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) |
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Pages (from-to) | 1533-1550 |
Number of pages | 18 |
Journal | Letters in Mathematical Physics |
Volume | 105 |
Issue number | 11 |
DOIs | |
State | Published - Nov 1 2015 |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics