Classification of Thurston Maps – Anastasia Shepelevtseva (Scuola Normale Superiore)

Abstract

Aula M1 Polo Fibonacci Abstract: Let f : S^2 –>S^2 be an orientation preserving branched covering of degree 2. The map f has two critical points c_1(f) and c_2(f). Let v_1(f) and v_2(f) be the corresponding critical values. The post-critical set of f is defined as the smallest closed f-stable set including v_1(f) and v_2(f). The post-critical set of f will be denoted by P(f). If P(f) is finite, then f is said to be post-critically finite. Thurston map is a post-critically finite orientation preserving branched covering. In my talk I will only consider degree two Thurston maps. An important invariant of a Thurston map is its iterated monodromy group (IMG). It gives a detailed, and often complete, characterization of the corresponding Thurston equivalence class. I will define the Thurston equivalence and IMG properly and I will also sketch the algorithm which translates a combinatorial presentation of a branched covering using invariant graph containing the post-critical set into an explicit presentation of its IMG. Sito web: http://people.dm.unipi.it/babygeometri/

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