Bott-integrable Reeb flows on 3-manifolds
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929209213976576 |
|---|---|
| author | Geiges, Hansjörg Hedicke, Jakob Sağlam, Murat |
| author_facet | Geiges, Hansjörg Hedicke, Jakob Sağlam, Murat |
| contents | This paper is devoted to studying a notion of Bott integrability for Reeb flows on contact 3-manifolds. We show, in analogy with work of Fomenko-Zieschang on Hamiltonian flows in dimension 4, that Bott-integrable Reeb flows exist precisely on graph manifolds. We also show that all $S^1$-invariant contact structures on Seifert manifolds, as well as all contact structures on the 3-sphere, on the 3-torus, and on $S^1\times S^2$, admit Bott-integrable Reeb flows. Along the way, we establish some general Liouville-type theorems for Bott-integrable Reeb flows, and a number of topological constructions (connected sum, open books, Dehn surgery) that may be expected to have wider applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07701 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bott-integrable Reeb flows on 3-manifolds Geiges, Hansjörg Hedicke, Jakob Sağlam, Murat Symplectic Geometry Dynamical Systems 37J35, 37J55, 53D35, 57K33 This paper is devoted to studying a notion of Bott integrability for Reeb flows on contact 3-manifolds. We show, in analogy with work of Fomenko-Zieschang on Hamiltonian flows in dimension 4, that Bott-integrable Reeb flows exist precisely on graph manifolds. We also show that all $S^1$-invariant contact structures on Seifert manifolds, as well as all contact structures on the 3-sphere, on the 3-torus, and on $S^1\times S^2$, admit Bott-integrable Reeb flows. Along the way, we establish some general Liouville-type theorems for Bott-integrable Reeb flows, and a number of topological constructions (connected sum, open books, Dehn surgery) that may be expected to have wider applications. |
| title | Bott-integrable Reeb flows on 3-manifolds |
| topic | Symplectic Geometry Dynamical Systems 37J35, 37J55, 53D35, 57K33 |
| url | https://arxiv.org/abs/2302.07701 |