Strong Nielsen equivalence on the punctured disc
speaker: Stavroula Makri (Uniwersytet MikoĊaja Kopernika w Toruniu)abstract: A classical problem related to Nielsen theory deals with the question of determining the minimum number of fixed points among all maps homotopic to a given continuous map f from a compact space to itself. This problem motivated the definition of an equivalence relation on the set of fixed points of f separating the fixed points into Nielsen equivalence classes. In this talk we will focus on the strong Nielsen equivalence, which is a "stronger" equivalence relation concerning periodic points of a surface homeomorphism. We will focus on orientation-preserving homeomorphisms of the 2-disc D2that fix the boundary pointwise and leave invariant a finite subset in the interior of D2. We will study the strong Nielsen equivalence of periodic points of such homeomorphisms f and we will give a necessary and sufficient condition for two periodic points to be strong Nielsen equivalent, with respect to the given f-invariant set, in the context of braid group theory.
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