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Mega-bimodules of topological polynomials: sub-hyperbolicity and Thurston obstructions

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Title: Mega-bimodules of topological polynomials: sub-hyperbolicity and Thurston obstructions
Author(s): Kelsey, Gregory A.
Director of Research: Kapovich, Ilya
Doctoral Committee Chair(s): Merenkov, Sergiy A.
Doctoral Committee Member(s): Kapovich, Ilya; Leininger, Christopher J.; Athreya, Jayadev S.
Department / Program: Mathematics
Discipline: Mathematics
Degree Granting Institution: University of Illinois at Urbana-Champaign
Degree: Ph.D.
Genre: Dissertation
Subject(s): Combinatorics of complex dynamics self-similar groups
Abstract: In 2006, Bartholdi and Nekrashevych solved a decade-old problem in holomorphic dynamics by creatively applying the theory of self-similar groups. Nekrashevych expanded this work in 2009 to define what we refer to as mega-bimodules which capture the topological data of Hurwitz classes of topological polynomials. He also showed that proving that these mega-bimodules are sub-hyperbolic will have two important implications: that all iterated monodromy groups of topological polynomials are contracting and that the Hubbard- Schliecher spider algorithm for complex polynomials generalizes to topological polynomials. We prove sub- hyperbolicity in the simplest non-trivial case and apply these mega-bimodules to holomorphic dynamics to prove a partial converse to the Berstein-Levy Theorem proved in 1985.
Issue Date: 2011-05-25
URI: http://hdl.handle.net/2142/24082
Rights Information: Copyright 2011 Gregory A. Kelsey
Date Available in IDEALS: 2011-05-25
Date Deposited: 2011-05
 

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