Recognizing critically fixed Thurston maps

I2M, Luminy, Marseille

Date(s) : 05/11/2021   iCal
11 h 00 min - 12 h 30 min

In 1980’s Fields medalist William Thurston obtained his celebrated characterization of rational mappings. This result is one of the most important and influential results in modern complex dynamics. It laid the foundation of such a field as Thurston theory of holomorphic maps, which has been actively developing in the last few decades. One of the most important problems in this area are questions about characterization, which is understanding when a topological map is equivalent to a holomorphic one, and classification, which is enumeration of all possible topological models of holomorphic maps from a given class. This work contributes to Thurston theory by investigating the class of critically fixed rational maps.

We will discuss the characterization, classification, and twisting problems for the class of rational maps having all their critical points fixed. In particular, we will present an algorithm that checks whether a given critically fixed Thurston map is realizable, and if so, describes its combinatorial model given by a planar graph on the sphere. This algorithm can be used to solve the twisting problem in the class of critically fixed rational maps.


FRUMAM, St Charles (3ème étage)


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