Journal of Modern Dynamics (JMD)

Topological characterization of canonical Thurston obstructions

Pages: 99 - 117, Issue 1, March 2013      doi:10.3934/jmd.2013.7.99

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Nikita Selinger - Institute for Mathematical Sciences, Stony Brook University, Stony Brook, NY 11794-3660, United States (email)

Abstract: Let $f$ be an obstructed Thurston map with canonical obstruction $\Gamma_f$. We prove the following generalization of Pilgrim's conjecture: if the first-return map $F$ of a periodic component $C$ of the topological surface obtained from the sphere by pinching the curves of $\Gamma_f$ is a Thurston map then the canonical obstruction of $F$ is empty. Using this result, we give a complete topological characterization of canonical Thurston obstructions.

Keywords:  Canonical Thurston obstructions, Thurston's characterization theorem for rational maps.
Mathematics Subject Classification:  Primary: 37F20, 37F30; Secondary: 32G15.

Received: August 2012;      Available Online: May 2013.