Mathematics – Symplectic Geometry
Scientific paper
2004-04-30
Mathematics
Symplectic Geometry
45 pages
Scientific paper
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.
No associations
LandOfFree
Floer homology, symplectic and complex hyperbolicities does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Floer homology, symplectic and complex hyperbolicities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Floer homology, symplectic and complex hyperbolicities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-287294