Constructive Geometrization of Thurston Maps and Decidability of Thurston Equivalence

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• 作者：Nikita Selinger ; Michael Yampolsky
• 关键词：Thurston equivalence ; Thurston obstruction ; Lattès map ; Geometrization
• 刊名：Arnold Mathematical Journal
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：1
• 期：4
• 页码：361-402
• 全文大小：1,017 KB
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• 作者单位：Nikita Selinger (1)
  Michael Yampolsky (2)
  
  1. Department of Mathematics, University of Alabama at Birmingham, CH 452, 1300 University Blvd, Birmingham, AL, 35294-1170, USA
  2. Mathematics Department, University of Toronto, 40 St George Street, Toronto, Ontario, M5S2E4, Canada
  
• 刊物类别：Mathematics, general; Algebraic Geometry; Mathematical Physics; Analysis; Dynamical Systems and Ergo
• 刊物主题：Mathematics, general; Algebraic Geometry; Mathematical Physics; Analysis; Dynamical Systems and Ergodic Theory; Combinatorics;
• 出版者：Springer International Publishing
• ISSN：2199-6806

文摘

The key result in the present paper is a direct analogue of the celebrated Thurston’s Theorem Douady and Hubbard (Acta Math 171:263-97, 1993) for marked Thurston maps with parabolic orbifolds. Combining this result with previously developed techniques, we prove that every Thurston map can be constructively geometrized in a canonical fashion. As a consequence, we give a partial resolution of the general problem of decidability of Thurston equivalence of two postcritically finite branched covers of \(S^2\) (cf. Bonnot et al. Moscow Math J 12:747-63, 2012). Keywords Thurston equivalence Thurston obstruction Lattès map Geometrization