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Twisted matings and equipotential gluings
Xavier Buff; Adam L. Epstein; Sarah Koch
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 21 (2012) no. S5, p. 995-1031

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.

Un outil crucial pour l’étude des fractions rationnelles post-critiquement finies est la caractérisation topologique des fractions rationnelles due à Thurston. La démonstration de ce théorème repose sur l’itération d’un endomorphisme holomorphe d’un certain espace de Teichmüller. Le graphe de cet endomorphisme revêt une correspondance au niveau de l’espace des modules. Dans des cas favorables, cette correspondance est le graphe d’une application qui peut être utilisée pour étudier les accouplements. Nous illustrons ceci par un exemple : nous étudions l’auto-accouplement de la basilique.

@article{AFST_2012_6_21_S5_995_0,
     author = {Xavier Buff and Adam L. Epstein and Sarah Koch},
     title = {Twisted matings and equipotential gluings},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 21},
     number = {S5},
     year = {2012},
     pages = {995-1031},
     doi = {10.5802/afst.1360},
     zbl = {06167099},
     mrnumber = {3088265},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2012_6_21_S5_995_0}
}
Buff, Xavier; Epstein, Adam L.; Koch, Sarah. Twisted matings and equipotential gluings. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 21 (2012) no. S5, pp. 995-1031. doi : 10.5802/afst.1360. https://afst.centre-mersenne.org/item/AFST_2012_6_21_S5_995_0/

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