
## 3. Thurston Rigidity

Problems related to Thurston Rigidity
1. ### Irreducibility of Gleason polynomials

#### 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

#### Problem 3.2.

[Adam Epstein] Algebraic proof of infinitesimal Thurston Rigidity, i.e. if $f$ is PCF non-Lattès 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.