Moment polytopes for symplectic manifolds with monodromy

2005/04/08 by San Vu Ngoc, Ngoc, San Vu · 2 citations
Mathematics · Physics and Astronomy · #37J15 #37J35 #53D05 #53D20 #57R45 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #msc:37J15 #msc:37J35 #msc:53D05 #msc:53D20 #msc:57R45

paper · pdf · doi:10.48550/arxiv.math/0504165

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

arxiv created 2005/04/08 · arxiv updated 2009/12/01

Abstract

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 S¹-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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• Delzant-type classification of near-symplectic toric 4-manifolds
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