# American Institute of Mathematical Sciences

January  2013, 7(1): 99-117. doi: 10.3934/jmd.2013.7.99

## Topological characterization of canonical Thurston obstructions

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

Received  August 2012 Published  May 2013

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.
Citation: Nikita Selinger. Topological characterization of canonical Thurston obstructions. Journal of Modern Dynamics, 2013, 7 (1) : 99-117. doi: 10.3934/jmd.2013.7.99
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