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Title: | Mega-bimodules of topological polynomials: sub-hyperbolicity and Thurston obstructions |
Author(s): | Kelsey, Gregory A. |
Director of Research: | Kapovitch, Ilia |
Doctoral Committee Chair(s): | Merenkov, Sergiy A. |
Doctoral Committee Member(s): | Kapovitch, Ilia; 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 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois