Floer homology, symplectic and complex hyperbolicities
| dc.creator | Biolley, Anne-Laure | |
| dc.date | 2004-04-30 | |
| dc.date.accessioned | 2026-07-07T05:07:50Z | |
| dc.date.available | 2026-07-07T05:07:50Z | |
| dc.description | On one side, from the properties of Floer cohomology, invariant associated to a symplectic manifold, we define and study a notion of symplectic hyperbolicity and a symplectic capacity measuring it. On the other side, the usual notions of complex hyperbolicity can be straightforwardly generalized to the case of almost-complex manifolds by using pseudo-holomorphic curves. That's why we study the links between these two notions of hyperbolicities when a manifold is provided with some compatible symplectic and almost-complex structures. We mainly explain how the non-symplectic hyperbolicity implies the existence of pseudo-holomorphic curves, and so the non-complex hyperbolicity. Thanks to this analysis, we could both better understand the Floer cohomology and get new results on almost-complex hyperbolicity. We notably prove results of stability for non-complex hyperbolicity under deformation of the almost-complex structure among the set of the almost-complex structures compatible with a fixed non-hyperbolic symplectic structure, thus generalizing Bangert theorem that gave this same result in the special case of the standard torus. | |
| dc.description | 45 pages | |
| dc.identifier | https://arxiv.org/abs/math/0404551 | |
| dc.identifier | http://arxiv.org/abs/math/0404551 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71019 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 53D40; 32Q60; 32Q65; 32Q68 | |
| dc.title | Floer homology, symplectic and complex hyperbolicities | |
| dc.type | text |