Properties of contact toric structures and concave boundaries of linear plumbings
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916566844571648 |
|---|---|
| author | Marinković, Aleksandra Nelson, Jo Rechtman, Ana Starkston, Laura Tanny, Shira Wang, Luya |
| author_facet | Marinković, Aleksandra Nelson, Jo Rechtman, Ana Starkston, Laura Tanny, Shira Wang, Luya |
| contents | We consider plumbings of symplectic disk bundles over spheres admitting concave contact boundary, with the goal of understanding the geometric properties of the boundary contact structure in terms of the data of the plumbing. We focus on the linear plumbing case in this article. We study the properties of the contact structure using two different sets of tools. First, we prove that all such contact manifolds have a global contact toric structure, and use tools from toric geometry to identify when the contact structure is tight versus overtwisted. Second, we study algebraic torsion measurements from embedded contact homology for these concavely induced contact manifolds, which has largely been unexplored. We develop a toolkit establishing existence and constraints of pseudoholomorphic curves adapted to the Morse-Bott Reeb dynamics of these plumbing examples, to provide the algebraic torsion and contact invariant calculations for the concave boundaries of linear plumbings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Properties of contact toric structures and concave boundaries of linear plumbings Marinković, Aleksandra Nelson, Jo Rechtman, Ana Starkston, Laura Tanny, Shira Wang, Luya Symplectic Geometry Geometric Topology We consider plumbings of symplectic disk bundles over spheres admitting concave contact boundary, with the goal of understanding the geometric properties of the boundary contact structure in terms of the data of the plumbing. We focus on the linear plumbing case in this article. We study the properties of the contact structure using two different sets of tools. First, we prove that all such contact manifolds have a global contact toric structure, and use tools from toric geometry to identify when the contact structure is tight versus overtwisted. Second, we study algebraic torsion measurements from embedded contact homology for these concavely induced contact manifolds, which has largely been unexplored. We develop a toolkit establishing existence and constraints of pseudoholomorphic curves adapted to the Morse-Bott Reeb dynamics of these plumbing examples, to provide the algebraic torsion and contact invariant calculations for the concave boundaries of linear plumbings. |
| title | Properties of contact toric structures and concave boundaries of linear plumbings |
| topic | Symplectic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2501.08451 |