Symplectic topology as the geometry of generating functions.
Symplectic topology of integrable hamiltonian systems, I : Arnold-Liouville with singularities
Symplectic torus actions with coisotropic principal orbits
In this paper we completely classify symplectic actions of a torus on a compact connected symplectic manifold when some, hence every, principal orbit is a coisotropic submanifold of . That is, we construct an explicit model, defined in terms of certain invariants, of the manifold, the torus action and the symplectic form. The invariants are invariants of the topology of the manifold, of the torus action, or of the symplectic form.In order to deal with symplectic actions which are not Hamiltonian,...
Symplectomorphism groups and isotropic skeletons.
The discriminant and oscillation lengths for contact and Legendrian isotopies
We define an integer-valued non-degenerate bi-invariant metric (the discriminant metric) on the universal cover of the identity component of the contactomorphism group of any contact manifold. This metric has a very simple geometric definition, based on the notion of discriminant points of contactomorphisms. Using generating functions we prove that the discriminant metric is unbounded for the standard contact structures on and . On the other hand we also show by elementary arguments that the...
The geography of simply-connected symplectic manifolds
By using the Seiberg-Witten invariant we show that the region under the Noether line in the lattice domain is covered by minimal, simply connected, symplectic 4-manifolds.
The Gromov width of complex Grassmannians.
The image in of the set of closed 2-forms with preassigned kernel
The symplectic Thom conjecture.
Three dimensional contact metric manifolds with vanishing Jacobi operator.
Transverse contact structures on Seifert 3-manifolds.
Une structure de contact, même tendue, est plus ou moins tordue