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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2025
1. Verfasser: Irmer, Ingrid
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2025
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/213195
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
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

Institution

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.
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