Séminaire de géométrie symplectique et de contact (archives)

We define fractional twists, a generalization of Dehn twists, for higher dimensional symplectic manifolds and look at some of their properties using contact topological methods. In particular, we will describe their role in invariant contact structures and discuss the difference between right-handed and left-handed twists.

Rationally and polynomially convex domains in $\C^n$ are fundamental objects of study in the theory of functions of several complex variables. After defining and illustrating these notions, I will explain joint work with Y.Eliashberg giving a complete characterization of the possible topologies of such domains in complex dimension at least three. The proofs are based on recent progress in symplectic topology, most notably the h-principles for loose Legendrian knots and Lagrangian caps.

Joint work with YankI Lekili.

If we think of CP^3 as the space of triples of points on the sphere then the Chiang Lagrangian is the subspace of triples with centre of mass at the origin. We will see that it has non-vanishing Floer cohomology if and only if the coefficient ring has characteristic 5. This calculation is related to Hitchin's work on Poncelet polygons.

In this talk I will discuss some results and speculations about virtual properties of the fundamental group of compact Kaehler manifolds.

I will discuss a symplectic embedding problem for polydisks in dimension 4. Symplectic embeddings are a key phenomenon of symplectic rigidity. In the case I consider, the obstruction for embedding the polydisk comes from a certain Lagrangian torus and uses the theory of J-holomorphic foliations in dimension 4. This is joint work with Richard Hind.

Travail en commun avec Emmanuel Giroux. On étudiera les hypersurfaces de Donaldson dans le cas de la symplectisée d'une variété de contact.