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Groups of homeomorphisms of the line with a finite number of fixed points
Salle B318 (IMB)
The goal of my talk will be to address the question: "which groups of increasing homeomorphisms of the line have at most N fixed points?". This question already has a partial answer given by the Hölder's Theorem (for the case N=0) and the Solodov's Theorem (for the case N=1) which classifies, unless than a semi-conjugation, all the groups that satisfy this statement. However, this question was still completely open for cases N>1.
In this talk I will present a new result that classifies all the groups that satisfy the statement for the case N=2, and some new examples of groups with N>2. For that, it will be necessary to introduce the concept of Orbit Opening as a semi-conjugation of groups of homeomorphisms, and the complete statements of Hölder's and Solodov's Theorems.