Geodesic
Toric structures on near-symplectic 4-manifolds
Journal of the European Mathematical Society, Tome 11 (2009) no. 3, pp. 487-520.

Voir la notice de l'article provenant de la source EMS Press

A near-symplectic structure on a 4-manifold is a closed 2-form that is symplectic away from the 1-dimensional submanifold along which it vanishes and that satisfies a certain transversality condition along this vanishing locus. We investigate near-symplectic 4-manifolds equipped with singular Lagrangian torus fibrations which are locally induced by effective Hamiltonian torus actions. We show how such a structure is completely characterized by a singular integral affine structure on the base of the fibration whenever the vanishing locus is nonempty. The base equipped with this geometric structure generalizes the moment map image of a toric 4-manifold in the spirit of earlier work by the second author on almost toric symplectic 4-manifolds. We use the geometric structure on the base to investigate the problem of making given smooth torus actions on 4-manifolds symplectic or Hamiltonian with respect to near-symplectic structures and to give interesting constructions of structures which are locally given by torus actions but have nontrivial global monodromy.
DOI : 10.4171/jems/157
Classification : 57-XX, 00-XX
Keywords: Symplectic, near-symplectic, toric, torus action, four-manifold, Hamiltonian, Lagrangian fibration 
@article{JEMS_2009_11_3_a1,
     author = {David T. Gay and Margaret Symington},
     title = {Toric structures on near-symplectic 4-manifolds},
     journal = {Journal of the European Mathematical Society},
     pages = {487--520},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2009},
     doi = {10.4171/jems/157},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/157/}
}
TY  - JOUR
AU  - David T. Gay
AU  - Margaret Symington
TI  - Toric structures on near-symplectic 4-manifolds
JO  - Journal of the European Mathematical Society
PY  - 2009
SP  - 487
EP  - 520
VL  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/157/
DO  - 10.4171/jems/157
ID  - JEMS_2009_11_3_a1
ER  - 
%0 Journal Article
%A David T. Gay
%A Margaret Symington
%T Toric structures on near-symplectic 4-manifolds
%J Journal of the European Mathematical Society
%D 2009
%P 487-520
%V 11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/157/
%R 10.4171/jems/157
%F JEMS_2009_11_3_a1
David T. Gay; Margaret Symington. Toric structures on near-symplectic 4-manifolds. Journal of the European Mathematical Society, Tome 11 (2009) no. 3, pp. 487-520. doi : 10.4171/jems/157. http://geodesic.mathdoc.fr/articles/10.4171/jems/157/

Cité par Sources :