11:00 Marcelo Ribeiro de Resende Alves (Bruxelles)
Legendrian contact homology and topological entropy.
Abstract: In this talk I will present certain results that show how Legendrian contact homology can be used to obtain estimates for the topological entropy of Reeb vector fields. The first connection between symplectic invariants and topological entropy appears in the works of Frauenfelder, Macarini and Schlenk; they used Lagrangian Floer homology to obtain positivity of topological entropy for symplectomorphisms on cotangent bundles and smooth Reeb flows in the unit tangent bundle of a manifold with "complicated" topology.Building on their work, we substitute their use of Lagrangian Floer homology by a version of Legendrian contact homology. This invariant has the advantages of being both more natural and more general for the study of Reeb flows, and to allow estimates for topological entropy in the case of finite differentiability. As an application, we obtain many new examples of contact 3-manifolds on which every Reeb flow has positive topological entropy.
Cobordisme Lagrangien exact et pseudo-isotopie.
Abstract: Considérons une paire des sous-variétés lagrangiennes L, L' dans une variété symplectique M. Un cobordisme lagrangien (W; L, L') est un cobordisme lisse W entre L et L' qui admet un plongement lagrangien dans la variété symplectique [0,1] x IR x M, et tel qu'il existe un \epsilon > 0 pour le quel W est donnée par [0, \epsilon) x {1} x L et (1- \epsilon, 1] x {1} x L' près du bord.
Dans cet exposé nous montrerons que sous des hypothèses topologiques additionnelles, un cobordisme Lagrangien exact (W; L, L') avec dim(W)>5 est une pseudo-isotopie (il est difféomorphe au produit [0,1]\times L).
16:00 Simon Schatz (Strasbourg)
A topological constraint for monotone Lagrangians in certain Kähler hypersurfaces..
Abstract: I establish a topological constraint for monotone Lagrangian embeddings in certain complex hypersurfaces of integral Kähler manifolds. As an application, we prove that it is impossible to embed a connected sum of (S^1 × S^2k)s in CP2k+1 as a monotone Lagrangian.
Prochaines séances: 17/04.
