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arXiv · 1005.4904

Mapping schemes realizable by obstructed topological polynomials

Gregory A. Kelsey
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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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Gregory A. Kelsey. 2010-05-26. Mapping schemes realizable by obstructed topological polynomials. https://arxiv.org/abs/1005.4904

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