# Toric structures on near-symplectic 4-manifolds

David T. Gay; Margaret Symington

Journal of the European Mathematical Society (2009)

- Volume: 011, Issue: 3, page 487-520
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topGay, David T., and Symington, Margaret. "Toric structures on near-symplectic 4-manifolds." Journal of the European Mathematical Society 011.3 (2009): 487-520. <http://eudml.org/doc/277606>.

@article{Gay2009,

abstract = {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.},

author = {Gay, David T., Symington, Margaret},

journal = {Journal of the European Mathematical Society},

keywords = {symplectic; near-symplectic; toric; torus action; four-manifold; Hamiltonian; Lagrangian fibration; symplectic; near-symplectic; toric; torus action; 4-manifold; Hamiltonian; Lagrangian fibration},

language = {eng},

number = {3},

pages = {487-520},

publisher = {European Mathematical Society Publishing House},

title = {Toric structures on near-symplectic 4-manifolds},

url = {http://eudml.org/doc/277606},

volume = {011},

year = {2009},

}

TY - JOUR

AU - Gay, David T.

AU - Symington, Margaret

TI - Toric structures on near-symplectic 4-manifolds

JO - Journal of the European Mathematical Society

PY - 2009

PB - European Mathematical Society Publishing House

VL - 011

IS - 3

SP - 487

EP - 520

AB - 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.

LA - eng

KW - symplectic; near-symplectic; toric; torus action; four-manifold; Hamiltonian; Lagrangian fibration; symplectic; near-symplectic; toric; torus action; 4-manifold; Hamiltonian; Lagrangian fibration

UR - http://eudml.org/doc/277606

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.