Différences

Ci-dessous, les différences entre deux révisions de la page.

--- pseudoholomorphic_curve_theory [2017/07/19 17:43]
niederkruger
+++ pseudoholomorphic_curve_theory [2017/07/21 14:48] (Version actuelle)
niederkruger
@@ Ligne 1: / Ligne 1: @@
 === Pseudo holomorphic curves ===
-Since Gromov published his '85 paper, pseudo-holomorphic curves have been one of the main tool in symplectic topology to prove "rigidity".
+Ever since Gromov published his '85 paper, pseudo-holomorphic curves have been one of the main tools in symplectic topology to prove "rigidity" results.
 Discussions related to holomorphic curves could be inspired by the following theorem in dimension 3.
@@ Ligne 11: / Ligne 11: @@
-Could something else be proved with holomorphic curves.  Should one consider holomorphic curves in the leaves of the foliation?  Should one do the symplectization of the foliated manifold to study holomorphic curves there like in an SFT-style?
+Could some similar result be proved with holomorphic curves?  Even if it is not possible to state such a result directly using only topological notions like fundamental groups or homology, maybe one could still define some type of Floer type invariants for symplectic foliations to get a generalization of the Novikov statement.
+Should one consider holomorphic curves in the leaves of the foliation?  Should one do the symplectization of the foliated manifold to study holomorphic curves there like in an SFT-style?

symp-foliations