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arXiv · 1706.09935

Faithful Semitoric Systems

Sonja Hohloch·Silvia Sabatini·Daniele Sepe·Margaret Symington
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Abstract

This paper consists of two parts. The first provides a review of the basic properties of integrable and almost-toric systems, with a particular emphasis on the integral affine structure associated to an integrable system. The second part introduces faithful semitoric systems, a generalization of semitoric systems (introduced by Vu Ngoc and classified by Pelayo and Vu Ngoc) that provides the language to develop surgeries on almost-toric systems in dimension 4. We prove that faithful semitoric systems are natural building blocks of almost-toric systems. Moreover, we show that they enjoy many of the properties that their (proper) semitoric counterparts do.

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Sonja Hohloch, Silvia Sabatini, Daniele Sepe, Margaret Symington. 2017-06-29. Faithful Semitoric Systems. https://doi.org/10.3842/sigma.2018.084

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