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An algebraic characterization of expanding Thurston maps

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  • Let $f\colon S^2 \to S^2$ be a postcritically finite branched covering map without periodic branch points. We give necessary and sufficient algebraic conditions for $f$ to be homotopic, relative to its postcritical set, to an expanding map $g$.
    Mathematics Subject Classification: Primary: 37F20; Secondary: 37D20, 20E08, 20F65, 54E40.


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