We provide a simple characterization of codimension two submanifolds of ${\mathbb{P}}^n\left(ℝ\right)$ that are of algebraic type, and use this criterion to provide examples of transcendental submanifolds when $n\ge 6$. If the codimension two submanifold is a nonsingular algebraic subset of ${\mathbb{P}}^n\left(ℝ\right)$ whose Zariski closure in ${\mathbb{P}}^n\left(ℂ\right)$ is a nonsingular complex algebraic set, then it must be an algebraic complete intersection in ${\mathbb{P}}^n\left(ℝ\right)$.

It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation ${ℱ}_G$. A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing $C^r$ diffeomorphism group G is simple iff the foliation ${ℱ}_{[G,G]}$ defined by [G,G] admits no proper minimal sets....

Dans ce texte, on définit, pour les immersions lagrangiennes de variétés fermées dans ${ℂ}^n$, une notion d’aire symplectique enlacée. Puis on construit, dans le cas $n=2$, un certain nombre de surfaces lagrangiennes enlaçant une aire infinie. Dans le cas des surfaces exactes, elles ont le minimum de points doubles possible permis par la théorie (sauf la sphère), c’est-à-dire moins que prévu par quelques conjectures.