Moment polytopes for symplectic manifolds with monodromy

Details Moment polytopes for symplectic manifolds with monodromy Moment polytopes for symplectic manifolds with monodromy

2005-04-08

arxiv.org/abs/math/0504165v1

Mathematics

Symplectic Geometry

finally a revision of the 2003 preprint. 29 pages, 8 figures

Scientific paper

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.

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