Recognizing topological polynomials by lifting trees
| Autor: | James Belk, Justin Lanier, Dan Margalit, Rebecca R. Winarski |
|---|---|
| Rok vydání: | 2019 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1906.07680 |
| Popis: | 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. Comment: 57 pages, 32 figures; accepted to Duke Mathematical Journal |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|