Anosov flows and Liouville pairs in dimension three
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909668674109440 |
|---|---|
| author | Massoni, Thomas |
| author_facet | Massoni, Thomas |
| contents | Building upon the work of Mitsumatsu and Hozoori, we establish a complete homotopy correspondence between three-dimensional Anosov flows and certain pairs of contact forms that we call Anosov Liouville pairs. We show a similar correspondence between projectively Anosov flows and bi-contact structures, extending the work of Mitsumatsu and Eliashberg-Thurston. As a consequence, every Anosov flow on a closed oriented three-manifold $M$ gives rise to a Liouville structure on $\mathbb{R} \times M$ which is well-defined up to homotopy, and which only depends on the homotopy class of the Anosov flow. Our results also provide a new perspective on the classification problem of Anosov flows in dimension three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_11036 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Anosov flows and Liouville pairs in dimension three Massoni, Thomas Symplectic Geometry Dynamical Systems Building upon the work of Mitsumatsu and Hozoori, we establish a complete homotopy correspondence between three-dimensional Anosov flows and certain pairs of contact forms that we call Anosov Liouville pairs. We show a similar correspondence between projectively Anosov flows and bi-contact structures, extending the work of Mitsumatsu and Eliashberg-Thurston. As a consequence, every Anosov flow on a closed oriented three-manifold $M$ gives rise to a Liouville structure on $\mathbb{R} \times M$ which is well-defined up to homotopy, and which only depends on the homotopy class of the Anosov flow. Our results also provide a new perspective on the classification problem of Anosov flows in dimension three. |
| title | Anosov flows and Liouville pairs in dimension three |
| topic | Symplectic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2211.11036 |