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

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Kelsey, Gregory A.

Contributors dc:contributor

• Kapovitch, Ilia
• Merenkov, Sergiy A.
• Leininger, Christopher J.
• Athreya, Jayadev S.

• Combinatorics of complex dynamics
• self-similar groups

Statement dc:rights

• Copyright 2011 Gregory A. Kelsey

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/24082

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/24082