A classical problem in Nielsen theory concerns determining the minimum number of fixed points among all maps homotopic to a given continuous self-map f of a compact space. This problem motivated the definition of an equivalence relation on the set of fixed points of f dividing them into Nielsen equivalence classes.
In this talk, we will focus on strong Nielsen equivalence, which is a ”stronger” equivalence relation that deals with periodic points of a surface homeomorphism. Specifically, we will consider orientation-preserving homeomorphisms of the 2-disc. We will study the strong Nielsen equivalence of periodic points of such homeomorphisms and we will give a necessary and sufficient condition for periodic points to be strong Nielsen equivalent in the context of braid theory.
