2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163933The purpose of this mostly expository paper is to discuss a connection between Nielsen fixed point theory and symplectic Floer homology theory for symplectomorphisms of surface and a calculation of Seidel's symplectic Floer homology for different mapping classes. We also describe symplectic zeta functions and asympltotic symplectic invariant. A generalisation of the Poincare- Birkhoff fixed point theorem and Arnold conjecture is proposed.25 pagesSymplectic GeometryGeometric Topology53D40; 37C30;text