Twisted matings and equipotential gluings
Xavier Buff, Adam L. Epstein, Sarah Koch (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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One crucial tool for studying postcritically finite rational maps is Thurston’s topological characterization of rational maps. This theorem is proved by iterating a holomorphic endomorphism on a certain Teichmüller space. The graph of this endomorphism covers a correspondence on the level of moduli space. In favorable cases, this correspondence is the graph of a map, which can be used to study matings. We illustrate this by way of example: we study the mating of the basilica with itself. ...