Nielsen Theory, Floer Homology and a Generalisation of the Poincaré-Birkhoff Theorem
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.
Fel'shtyn, Alexander. (2008). "Nielsen Theory, Floer Homology and a Generalisation of the Poincaré-Birkhoff Theorem". Journal of Fixed Point Theory and Applications, 3(2), 191-214. http://dx.doi.org/10.1007/s11784-008-0085-2