Title

Nielsen Theory, Floer Homology and a Generalisation of the Poincaré-Birkhoff Theorem

Document Type

Article

Publication Date

9-1-2008

Abstract

The purpose of this mostly expository paper is to discuss a connection between Nielsen fixed point theory and symplectic Floer homology for symplectomorphisms of surfaces and a calculation of Seidel’s symplectic Floer homology for different mapping classes. We also describe symplectic zeta functions and an asymptotic symplectic invariant. A generalisation of the Poincaré-Birkhoff fixed point theorem and Arnold conjecture is proposed.