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Topological characterization of canonical Thurston obstructions

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  • 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.
    Mathematics Subject Classification: Primary: 37F20, 37F30; Secondary: 32G15.


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