C. R. Math. Rep. Acad. Sci. Canada Vol. 34 (3) 2012, pp. 65–78
September 30, 2012
Sylvain Bonnot, Instituto de Matemática e Estatística, Rua do Matão, 1010, Cidade Universitá́ria, São Paulo, SP, Brasil; e-mail: sylvain@ime.usp.br
Michael Yampolsky, Mathematics Department, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4; e-mail: yampol@math.toronto.edu
Abstract/Résumé:
We study canonical decompositions of postcritically-finite branched coverings of the 2-sphere, as defined by K. Pilgrim. We show that every hyperbolic cycle in the decomposition does not have a Thurston obstruction. It is thus Thurston equivalent to a rational map.
Nous étudions les décompositions canoniques de revêtements ramifiés de la sphère, avec ensembles post-critiques finis, ainsi que K. Pilgrim les a définies. Nous montrons qu’aucun cycle hyperbolique dans la décomposition n’a d’obstruction de Thurston. Par conséquent, un tel cycle est équivalent au sens de Thurston à une application rationnelle.
AMS Subject Classification: Combinatorics and topology 37F20
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