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arXiv · 1906.07680

Recognizing topological polynomials by lifting trees

James Belk·Justin Lanier·Dan Margalit·Rebecca R. Winarski
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Abstract

We give a simple algorithm that determines whether a given post-critically finite topological polynomial is Thurston equivalent to a polynomial. If it is, 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 post-critical points is arbitrarily large.

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James Belk, Justin Lanier, Dan Margalit, Rebecca R. Winarski. 2019-06-18. Recognizing topological polynomials by lifting trees. https://arxiv.org/abs/1906.07680

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