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3. Thurston Rigidity

Problems related to Thurston Rigidity

    1. Irreducibility of Gleason polynomials


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      Problem 3.1.

      Define the Gleason polynomials as the polynomials in $c$ such that $f_c(x) = x^2+c$ is post-critically finite.

      Are the Gleason polynomials irreducible?

        • Algebraic proof of Thurston rigidity


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          Problem 3.2.

          [Adam Epstein] Algebraic proof of infinitesimal Thurston Rigidity, i.e. if $f$ is PCF non-LatteĢ€s and degree at least 2, then $1$ is not an eigenvalue of $f^{\ast}:H^1(\mathbb{P}^1,\Theta_{P_f}) \to H^1(\mathbb{P}^1,\Theta_{P_f})$ where $P_f$ is the post-critical set and $\Theta$ is the sheaf of holomorphic vector fields with zeros along the post-critical set.

              Cite this as: AimPL: Postcritically finite maps in complex and arithmetic dynamics, available at http://aimpl.org/finitedynamics.