Faithful Semitoric Systems
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 with an integrable system. The second part introduces faithful semitoric systems, a generalization of s...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209766 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Faithful Semitoric Systems / S. Hohloch, S. Sabatini, D. Sepe, M. Symington // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 55 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 with an integrable system. The second part introduces faithful semitoric systems, a generalization of semitoric systems (introduced by Vũ Ngoc and classified by Pelayo and Vũ 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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| ISSN: | 1815-0659 |