Floer Homology, Nielsen Theory and Symplectic Zeta Functions

TL;DR

This paper explores the relationship between symplectic Floer homology and Nielsen fixed point theory, introducing new symplectic zeta functions and invariants, and linking their special values to Reidemeister torsions.

Contribution

It establishes a novel connection between symplectic Floer homology and Nielsen theory, and defines new symplectic zeta functions with significant invariants.

Findings

Symplectic zeta functions are introduced as new invariants.

Special values of these zeta functions relate to Reidemeister torsions.

A link between symplectic Floer homology and Nielsen fixed point theory is demonstrated.

Abstract

We describe a connection between symplectic Floer homology for symplectomorphisms of surface and Nielsen fixed point theory. A new zeta functions and asymptotic invariant of symplectic origin are defined. We show that special values of symplectic zeta functions are Reidemeister torsions.