Acta Mathematica

Thurston equivalence of topological polynomials

Laurent Bartholdi and Volodymyr Nekrashevych

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Abstract

We answer Hubbard's question on determining the Thurston equivalence class of “twisted rabbits”, i.e. composita of the “rabbit” polynomial with nth 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.

Article information

Source
Acta Math., Volume 197, Number 1 (2006), 1-51.

Dates
Received: 21 November 2005
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485891842

Digital Object Identifier
doi:10.1007/s11511-006-0007-3

Mathematical Reviews number (MathSciNet)
MR2285317

Zentralblatt MATH identifier
1176.37020

Rights
2006 © Institut Mittag-Leffler

Citation

Bartholdi, Laurent; Nekrashevych, Volodymyr. Thurston equivalence of topological polynomials. Acta Math. 197 (2006), no. 1, 1--51. doi:10.1007/s11511-006-0007-3. https://projecteuclid.org/euclid.acta/1485891842


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