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 |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209766 |
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| 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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Hohloch, S. Sabatini, S. Sepe, D. Symington, M. 2025-11-26T11:25:20Z 2018 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. 1815-0659 2010 Mathematics Subject Classification: 37J35; 37J05; 53D20; 70H06 arXiv: 1706.09935 https://nasplib.isofts.kiev.ua/handle/123456789/209766 https://doi.org/10.3842/SIGMA.2018.084 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. The authors would like to thank the anonymous referees for their careful reading of an earlier draft of this paper, as well as for their suggestions that have significantly improved the quality of the paper. Furthermore, the authors would like to thank Eva Miranda for providing comments on an earlier draft of this paper. S.H. was partially supported by the Research Fund of the University of Antwerp and by SwissMAP. S.S. was partially supported by SFB-TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics, funded by the Deutsche Forschungsgemeinschaft. D.S. was partially supported by the University of Cologne, SwissMAP, the NWO Veni grant 639.031.345, and by the CNPq Universal grant 409552/2016-0. M.S. was partially supported by Mercer University, the Institute of Pure and Applied Mathematics (IMPA) in Rio de Janeiro, the University of Cologne, and the Swiss Federal Institute of Technology (ETH) in Zurich. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Faithful Semitoric Systems Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Faithful Semitoric Systems |
| spellingShingle |
Faithful Semitoric Systems Hohloch, S. Sabatini, S. Sepe, D. Symington, M. |
| title_short |
Faithful Semitoric Systems |
| title_full |
Faithful Semitoric Systems |
| title_fullStr |
Faithful Semitoric Systems |
| title_full_unstemmed |
Faithful Semitoric Systems |
| title_sort |
faithful semitoric systems |
| author |
Hohloch, S. Sabatini, S. Sepe, D. Symington, M. |
| author_facet |
Hohloch, S. Sabatini, S. Sepe, D. Symington, M. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
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Інститут математики НАН України |
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Article |
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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 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209766 |
| citation_txt |
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. |
| work_keys_str_mv |
AT hohlochs faithfulsemitoricsystems AT sabatinis faithfulsemitoricsystems AT seped faithfulsemitoricsystems AT symingtonm faithfulsemitoricsystems |
| first_indexed |
2025-12-07T15:51:09Z |
| last_indexed |
2025-12-07T15:51:09Z |
| _version_ |
1850886104272601088 |