Topological characterization of canonical Thurston obstructions

Nikita Selinger

doi:10.3934/jmd.2013.7.99

Article Contents

2013, Volume 7, Issue 1: 99-117. Doi: 10.3934/jmd.2013.7.99

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Topological characterization of canonical Thurston obstructions

Nikita Selinger^1,

1.
Institute for Mathematical Sciences, Stony Brook University, Stony Brook, NY 11794-3660

Received: July 31, 2012

Published: April 2013

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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.

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