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 | |
| State | Published - Nov 1 2015 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
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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 journal › Article
TY - JOUR
T1 - Poisson Structures on Smooth 4–Manifolds
AU - García-Naranjo, Luis C.
AU - Suárez-Serrato, Pablo
AU - Vera, Ramón
PY - 2015/11/1
Y1 - 2015/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84943660316&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84943660316&partnerID=8YFLogxK
U2 - 10.1007/s11005-015-0792-8
DO - 10.1007/s11005-015-0792-8
M3 - Article
AN - SCOPUS:84943660316
VL - 105
SP - 1533
EP - 1550
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
SN - 0377-9017
IS - 11
ER -