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July 2020 A positive characterization of rational maps
Dylan P. Thurston
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Ann. of Math. (2) 192(1): 1-46 (July 2020). DOI: 10.4007/annals.2020.192.1.1

Abstract

When is a topological branched self-cover of the sphere equivalent to a post-critically finite rational map on $\mathbb{C}\mathbb{P}^1$? William Thurston gave one answer in 1982, giving a negative criterion (an obstruction to a map being rational). We give a complementary, positive criterion: the branched self-cover is equivalent to a rational map if and only if there is an elastic graph spine for the complement of the post-critical set that gets ``looser" under backwards iteration.

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Dylan P. Thurston. "A positive characterization of rational maps." Ann. of Math. (2) 192 (1) 1 - 46, July 2020. https://doi.org/10.4007/annals.2020.192.1.1

Information

Published: July 2020
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2020.192.1.1

Subjects:
Primary: 37F10
Secondary: 37E25 , 37F31

Keywords: complex dynamics , elastic graphs , extremal length , quasiconformal surgery , rational maps , Thurston obstruction

Rights: Copyright © 2020 Department of Mathematics, Princeton University

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Vol.192 • No. 1 • July 2020
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