Year: 2020
Type: article
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.
Source: Annals of Mathematics
Author: Dylan P. Thurston
Institution: Indiana University Bloomington
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2590189730