On Legendrian Thurston-Bennequin-symmetrical graphs
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910085410717696 |
|---|---|
| author | Chau, Trung Shah, Tanushree |
| author_facet | Chau, Trung Shah, Tanushree |
| contents | This article reviews the development of Legendrian graph theory in the standard contact 3-sphere ($S^3, ξ_{std}$). We provide a generalized criterion under which the total Thurston-Bennequin invariant of a Legendrian graph (sum of tb of all cycles of the Legendrian graph) can be computed from the tb of its smaller cycles. We verify this criterion for graphs with up to 9 vertices and construct infinite families of examples where it holds. We also present examples demonstrating that each condition in the criterion is necessary. Notably, the graphs satisfying this criterion exhibit a high degree of symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28487 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Legendrian Thurston-Bennequin-symmetrical graphs Chau, Trung Shah, Tanushree Geometric Topology This article reviews the development of Legendrian graph theory in the standard contact 3-sphere ($S^3, ξ_{std}$). We provide a generalized criterion under which the total Thurston-Bennequin invariant of a Legendrian graph (sum of tb of all cycles of the Legendrian graph) can be computed from the tb of its smaller cycles. We verify this criterion for graphs with up to 9 vertices and construct infinite families of examples where it holds. We also present examples demonstrating that each condition in the criterion is necessary. Notably, the graphs satisfying this criterion exhibit a high degree of symmetry. |
| title | On Legendrian Thurston-Bennequin-symmetrical graphs |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2603.28487 |