Moment polytopes for symplectic manifolds with monodromy
Vu Ngoc, San
HAL, hal-00004652 / Harvested from HAL
Text on HAL
A natural way of generalising Hamiltonian toric manifolds is to permit the presence of generic isolated singularities for the moment map. For a class of such "almost-toric 4-manifolds'' which admits a Hamiltonian $S^1$-action we show that one can associate a group of convex polygons that generalise the celebrated moment polytopes of Atiyah, Guillemin-Sternberg. As an application, we derive a Duistermaat-Heckman formula demonstrating a strong effect of the possible monodromy of the underlying integrable system.
Publié le : 2005-04-08
Classification:  symplectic geometry,  monodromy,  semi-toric,  circle action,  completely integrable systems,  Lagrangian fibration,  moment polytope,  Duistermaat-Heckman,  53D05,53D20,37J15,37J35,  [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG],  [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],  [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] 
@article{hal-00004652,
     author = {Vu Ngoc, San},
     title = {Moment polytopes for symplectic manifolds with monodromy},
     journal = {HAL},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00004652}
}

Vu Ngoc, San. Moment polytopes for symplectic manifolds with monodromy. HAL, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/hal-00004652/