The Morse-Smale Property of the Thurston Spine
The Thurston spine consists of the subset of Teichmüller space at which the set of shortest curves, the systoles, cuts the surface into polygons. The systole function is a topological Morse function on Teichmüller space. This paper studies the local properties of the Thurston spine and the smooth pi...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/213195 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | The Morse-Smale Property of the Thurston Spine. Ingrid Irmer. SIGMA 21 (2025), 027, 32 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862539564833308672 |
|---|---|
| author | Irmer, Ingrid |
| author_facet | Irmer, Ingrid |
| citation_txt | The Morse-Smale Property of the Thurston Spine. Ingrid Irmer. SIGMA 21 (2025), 027, 32 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The Thurston spine consists of the subset of Teichmüller space at which the set of shortest curves, the systoles, cuts the surface into polygons. The systole function is a topological Morse function on Teichmüller space. This paper studies the local properties of the Thurston spine and the smooth pieces out of which it is constructed. Some of these local properties are shown to have global consequences, for example, that the Thurston spine satisfies properties defined in terms of the systole function analogous to that of Morse-Smale complexes of (smooth) Morse functions on compact manifolds with boundary.
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| first_indexed | 2026-03-21T11:41:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213195 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:41:53Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Irmer, Ingrid 2026-02-16T16:38:22Z 2025 The Morse-Smale Property of the Thurston Spine. Ingrid Irmer. SIGMA 21 (2025), 027, 32 pages 1815-0659 2020 Mathematics Subject Classification: 57R99; 57M99 arXiv:2401.05734 https://nasplib.isofts.kiev.ua/handle/123456789/213195 https://doi.org/10.3842/SIGMA.2025.027 The Thurston spine consists of the subset of Teichmüller space at which the set of shortest curves, the systoles, cuts the surface into polygons. The systole function is a topological Morse function on Teichmüller space. This paper studies the local properties of the Thurston spine and the smooth pieces out of which it is constructed. Some of these local properties are shown to have global consequences, for example, that the Thurston spine satisfies properties defined in terms of the systole function analogous to that of Morse-Smale complexes of (smooth) Morse functions on compact manifolds with boundary. The author would like to thank Stavros Garoufalidis, Don Zagier, and a number of very helpful anonymous referees for comments that led to significant improvements. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Morse-Smale Property of the Thurston Spine Article published earlier |
| spellingShingle | The Morse-Smale Property of the Thurston Spine Irmer, Ingrid |
| title | The Morse-Smale Property of the Thurston Spine |
| title_full | The Morse-Smale Property of the Thurston Spine |
| title_fullStr | The Morse-Smale Property of the Thurston Spine |
| title_full_unstemmed | The Morse-Smale Property of the Thurston Spine |
| title_short | The Morse-Smale Property of the Thurston Spine |
| title_sort | morse-smale property of the thurston spine |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213195 |
| work_keys_str_mv | AT irmeringrid themorsesmalepropertyofthethurstonspine AT irmeringrid morsesmalepropertyofthethurstonspine |