Thurston equivalence of topological polynomials

Laurent Bartholdi Institut de Mathématiques B, École Polytechnique Fédérale de Lausanne Volodymyr Nekrashevych Department of Mathematics, Texas A&M University

TBD mathscidoc:1701.331974

Acta Mathematica, 197, (1), 1-51, 2005.11
We answer Hubbard's question on determining the Thurston equivalence class of “twisted rabbits”, i.e. composita of the “rabbit” polynomial with$n$th powers of the Dehn twists about its ears. The answer is expressed in terms of the 4-adic expansion of$n$. We also answer the equivalent question for the other two families of degree-2 topological polynomials with three post-critical points. In the process, we rephrase the questions in group-theoretical language, in terms of wreath recursions.
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  title={Thurston equivalence of topological polynomials},
  author={Laurent Bartholdi, and Volodymyr Nekrashevych},
  booktitle={Acta Mathematica},
Laurent Bartholdi, and Volodymyr Nekrashevych. Thurston equivalence of topological polynomials. 2005. Vol. 197. In Acta Mathematica. pp.1-51.
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