07/01/2014, 16:30 — 17:30 — Room P3.10, Mathematics Building
Sheila Sandon, CNRS/Nantes
An analogue in contact topology of the Arnold conjecture on fixed points of Hamiltonian diffeomorphismsThe Arnold conjecture in symplectic topology says that for every Hamiltonian diffeomorphism on a compact symplectic manifold the number of fixed points is at least equal to the minimal number of critical points of a function on the manifold. In my talk I will present an analogue in contact topology of this conjecture, based on the notion of translated points of contactomorphisms, and a work in progress to prove it by constructing a Floer homology theory for translated points. I will also briefly discuss how this is related to some other contact rigidity phenomena, discovered after the work of Eliashberg and Polterovich in 2000, such as the existence of partial orders and biinvariant metrics on the group of contactomorphisms.