15 November 2022 Recognizing topological polynomials by lifting trees
James Belk, Justin Lanier, Dan Margalit, Rebecca R. Winarski
Author Affiliations +
Duke Math. J. 171(17): 3401-3480 (15 November 2022). DOI: 10.1215/00127094-2022-0043

Abstract

We give a simple algorithm that determines whether a given postcritically finite topological polynomial is Thurston equivalent to a polynomial. If it is, then the algorithm produces the Hubbard tree; otherwise, the algorithm produces the canonical obstruction. Our approach is rooted in geometric group theory, using iteration on a simplicial complex of trees, and building on work of Nekrashevych. As one application of our methods, we resolve the polynomial case of Pilgrim’s finite global attractor conjecture. We also give a new solution to Hubbard’s twisted rabbit problem, and we state and solve several generalizations of Hubbard’s problem where the number of postcritical points is arbitrarily large.

Citation

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James Belk. Justin Lanier. Dan Margalit. Rebecca R. Winarski. "Recognizing topological polynomials by lifting trees." Duke Math. J. 171 (17) 3401 - 3480, 15 November 2022. https://doi.org/10.1215/00127094-2022-0043

Information

Received: 20 July 2020; Revised: 16 November 2021; Published: 15 November 2022
First available in Project Euclid: 18 October 2022

MathSciNet: MR4510015
zbMATH: 1515.37044
Digital Object Identifier: 10.1215/00127094-2022-0043

Subjects:
Primary: 37F20
Secondary: 57M10

Keywords: complex dynamics , Thurston’s theorem , topological polynomials , twisted rabbit problem

Rights: Copyright © 2022 Duke University Press

Vol.171 • No. 17 • 15 November 2022
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