Mapping schemes realizable by obstructed topological polynomials

Kelsey, Gregory

doi:10.1090/S1088-4173-2012-00239-1

Mapping schemes realizable by obstructed topological polynomials
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by Gregory A. Kelsey

Conform. Geom. Dyn. 16 (2012), 44-80

DOI: https://doi.org/10.1090/S1088-4173-2012-00239-1

Published electronically: March 13, 2012

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Abstract:

In 1985, Levy used a theorem of Berstein to prove that all hyperbolic topological polynomials are equivalent to complex polynomials. We prove a partial converse to the Berstein-Levy Theorem: given post-critical dynamics that are in a sense strongly non-hyperbolic, we prove the existence of topological polynomials which are not equivalent to any complex polynomial that realize these post-critical dynamics. This proof employs the theory of self-similar groups to demonstrate that a topological polynomial admits an obstruction and produces a wealth of examples of obstructed topological polynomials.

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