Unlinking and unknottedness of monotone Lagrangian submanifolds
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2012
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917718407512064 |
|---|---|
| author | Rizell, Georgios Dimitroglou Evans, Jonathan David |
| author_facet | Rizell, Georgios Dimitroglou Evans, Jonathan David |
| contents | Under certain topological assumptions, we show that two monotone Lagrangian submanifolds embedded in the standard symplectic vector space with the same monotonicity constant cannot link one another and that, individually, their smooth knot type is determined entirely by the homotopy theoretic data which classifies the underlying Lagrangian immersion. The topological assumptions are satisfied by a large class of manifolds which are realised as monotone Lagrangians, including tori. After some additional homotopy theoretic calculations, we deduce that all monotone Lagrangian tori in the symplectic vector space of odd complex dimension at least five are smoothly isotopic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1211_6633 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Unlinking and unknottedness of monotone Lagrangian submanifolds Rizell, Georgios Dimitroglou Evans, Jonathan David Symplectic Geometry Differential Geometry 53D12, 53D40, 53D42 Under certain topological assumptions, we show that two monotone Lagrangian submanifolds embedded in the standard symplectic vector space with the same monotonicity constant cannot link one another and that, individually, their smooth knot type is determined entirely by the homotopy theoretic data which classifies the underlying Lagrangian immersion. The topological assumptions are satisfied by a large class of manifolds which are realised as monotone Lagrangians, including tori. After some additional homotopy theoretic calculations, we deduce that all monotone Lagrangian tori in the symplectic vector space of odd complex dimension at least five are smoothly isotopic. |
| title | Unlinking and unknottedness of monotone Lagrangian submanifolds |
| topic | Symplectic Geometry Differential Geometry 53D12, 53D40, 53D42 |
| url | https://arxiv.org/abs/1211.6633 |