On Thurston's characterization theorem for branched covers

  • Let f be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map f of a finite-dimensional Teichmuller space. We prove that this map extends continuously to the augmented Teichmuller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichmuller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim and to infer further properties of Thurston's pullback map. We obtain a complete topological description of canonical obstructions. Our approach also yields new proofs of Thurston's theorem and Pilgrim's Canonical Obstruction theorem.

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Publishing Institution:IRC-Library, Information Resource Center der Jacobs University Bremen
Granting Institution:Jacobs Univ.
Author:Nikita Selinger
Referee:Dierk Schleicher, John Hubbard, Daniel Meyer, √Čtienne Ghys
Advisor:Dierk Schleicher
Persistent Identifier (URN):urn:nbn:de:101:1-2013052812102
Document Type:PhD Thesis
Date of Successful Oral Defense:2011/07/07
Year of Completion:2011
Date of First Publication:2011/08/04
PhD Degree:Mathematics
Library of Congress Classification:Q Science / QA Mathematics (incl. computer science)
School:SES School of Engineering and Science
Call No:Thesis 2011/26

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