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Classifying affine structures with focus-focus singularities

2024/01/19 by Tang, Xiudi
#53D20 (Primary) 53A15 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2401.10881

Abstract

We study the singular affine structures of integrable systems with focus-focus singular fibers on the image of momentum maps. The classification of singular affine structures is equivalent to the classification of simple semitoric systems up to fiber-preserving symplectomorphisms but is not equivalent for semitoric systems with multiple pinched fibers and we give counterexamples for any number of more than one pinch on each fiber.

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