# Geometria em Lisboa Seminar

### 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 diffeomorphisms

The 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.