Abstract

We refine Douady and Hubbard's proof of Thurston's topological characterization of rational functions by proving the following theorem. Let f: S2→S2 be a branched covering with finite postcritical set Pf and hyperbolic orbifold. Let Γc denote the set of all homotopy classes γ of nonperipheral, simple closed curves in S2-Pf such that the length of the unique geodesic homotopic to γ tends to zero under iteration of the Thurston map induced by f on Teichmüller space. Then either Γc is empty, and f is equivalent to a rational function, or else Γc is a Thurston obstruction. © 2001 Academic Press.

Department(s)

Mathematics and Statistics

Publication Status

Open Archive

Comments

National Science Foundation, Grant DMS 9996070

International Standard Serial Number (ISSN)

0001-8708

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Elsevier, All rights reserved.

Publication Date

25 Mar 2001

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