A positive characterization of rational maps

• 成果类型: Article
• 署名作者: Thurston, Dylan P.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2020.192.1.1
• 发表日期: 2020
• 页码: 1-46
• 关键词: curves

摘要

When is a topological branched self-cover of the sphere equivalent to a post-critically finite rational map on CP1? 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.