Toric structures on near-symplectic 4-manifolds
| dc.creator | Gay, David T. | |
| dc.creator | Symington, Margaret | |
| dc.date | 2006-09-27 | |
| dc.date.accessioned | 2026-07-07T07:25:17Z | |
| dc.date.available | 2026-07-07T07:25:17Z | |
| dc.description | 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. | |
| dc.description | 43 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/0609753 | |
| dc.identifier | http://arxiv.org/abs/math/0609753 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116669 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Geometric Topology | |
| dc.subject | 57R17 (Primary) 53D20, 57M60, 57M50 (Secondary) | |
| dc.title | Toric structures on near-symplectic 4-manifolds | |
| dc.type | text |