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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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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.

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.
Status:	Published
Refereed:	Yes
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:	0012-7094
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
Related URLs:	arXiv Publisher

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References

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Deposit and Record Details

ID Code:	280397
Depositing User:	Dr Jim Belk
Datestamp:	05 Oct 2022 11:33
Last Modified:	23 Nov 2022 13:57
Date of acceptance:	23 November 2021
Date of first online publication:	18 October 2022
Date Deposited:	5 October 2022
Data Availability Statement:	No