SS2 - Topologie et géométrie symplectiques / SS2 - Symplectic topology and geometry
Org: D. Auroux (MIT/X) et/and F. Lalonde (Montréal)

FRÉDÉRIC BOURGEOIS, Université Libre de Bruxelles
Homotopy groups of the space of contact structures

We show how the functorial properties of contact homology can be used to detect nontrivial elements in the homotopy groups of the space of contact structures. This technique will then be illustrated with various examples.

OCTAV CORNEA, Université de Montréal, CP 6128 Succ. Centre Ville, Montréal, Québec H3C 3J7, Canada
Cluster homology and detection of pseudoholomorphic disks and strips

In this talk I will review shortly the construction of the cluster homology of a Lagrangian submanifold and describe some applications to the detection of pseudoholomorphic disks (this part of the talk is based on joint work with Francois Lalonde). I will also indicate how this construction is related to a previous one-introduced jointly with Jean-Francois Barraud-which serves to detect algebraically pseudoholomorphic strips.

Toric and symplectic automorphism groups

Every toric manifold M has a natural automorphism group A that is a maximal compact subgroup of the symplectomorphism group S of M. I will discuss recent work due to Susan Tolman and myself concerning the relation between these groups. In particular I will discuss the question of when the induced map p1 (A) ® p1 (S) is injective. It turns out that toric manifolds for which injectivity fails have a very special structure.


CLAUDE VITERBO, Ecole Polytechnique, Palaiseau

JEAN-YVES WELSCHINGER, Ecole normale supérieure de Lyon, UMPA, 46, allée d'Italie, 69364 Lyon Cedex 07
Invariants of real symplectic 4-manifolds and lower bounds in real enumerative geometry

I will define invariants under deformation of real symplectic 4-manifolds. These invariants are obtained via an algebraic count of real rational J-holomorphic curves which pass through a given configuration of points, for a generic almost complex structure J. These invariants provide lower bounds in real enumerative geometry, namely for the total number of such real rational J-holomorphic curves.