Recognizing topological polynomials by lifting trees

Belk, J., Lanier, J., Margalit, D. and Winarski, R. R. (2022) Recognizing topological polynomials by lifting trees. Duke Mathematical Journal, 171(17), pp. 3401-3480. (doi: 10.1215/00127094-2022-0043)

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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.

Item Type:Articles
Additional Information:The first author was supported by EPSRC grant EP/R032866/1 and the National Science Foundation (NSF) under grant DMS-1854367. The second author was supported by NSF grant DGE-1650044. The third author was supported by NSF grant DMS-1745583. The fourth author was supported by NSF grant DMS-2002951.
Glasgow Author(s) Enlighten ID:Belk, Dr Jim
Authors: Belk, J., Lanier, J., Margalit, D., and Winarski, R. R.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Duke Mathematical Journal
Journal Abbr.:Duke Math. J.
Publisher:Duke University Press
ISSN (Online):1547-7398
Published Online:18 October 2022
Copyright Holders:Copyright © 2022 Duke University Press
First Published:First published in Duke Mathematical Journal 171(17):3401-3480
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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