Chennai Mathematical Institute


2.45 p.m.
The Arnold conjecture and Floer homology

Cedric Bounya
ENS, France.


We shall present the context of the conjecture by V.I. Arnol'd in the 1960's about the least number of fixed points a Hamiltonian symplectomorphism on a compact manifold must have, and will outline the main ideas of Floer's theory in a context as little technical as possible.

This theory builds a homology for compact symplectic manifolds, whose underlying complex is spanned by fixed points of a generic Hamiltonian symplectomorphism. It answers Arnol'd's question with brio but also raises questions as to what its natural generalizations actually compute.