Différences

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

--- existence_of_symplectic_foliations [2017/07/19 16:26]
niederkruger
+++ existence_of_symplectic_foliations [2017/08/29 17:13] (Version actuelle)
alvaro
@@ Ligne 1: / Ligne 1: @@
-According to Thurston every manifold with vanishing Euler characteristic admits a codimension 1 foliation.
+===== Existence of symplectic foliations =====
-According to Gromov every open manifold admits a symplectic structure.  Bertelson combined these in certain cases (what cases?).
+  * **(R.L. Fernandes, F. Presas, G. Meigniez)** Conjecture: Let M be a closed, odd-dimensional, simply--connected manifold. Then it does not admit a codimension-1 strong symplectic foliation. It is known by work of Mitsumatsu that the 5-sphere does admit a weak symplectic foliation. In dimension 3, the conjecture is true due to Novikov's theorem.
+  * **(A. Mori)** Conjecture: Let (M,F) be a codimension-1 oriented foliation on a closed odd dimensional manifold. If the space of leafwise closed non-degenerate 2-forms is non-empty and contains no closed forms, there exists a closed leaf.
+  * **(M. Bertelson, G. Meigniez)** Is there an analogue of Thurston's h--principle for symplectic foliations of codimension higher than 1?
-Can these results be combined to produce (at least a weak) symplectic foliation on closed manifolds (with a stable complex structure)?

symp-foliations