The Teichmüller space of a rational map immerses into moduli space

Matthieu Astorg (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We prove that the dynamical Teichmüller space of a rational map immerses into the space of rational maps of the same degree, answering a question of McMullen and Sullivan. This is achieved through a new description of the tangent and cotangent space to the dynamical Teichmüller space.

Mots clés: complex dynamics; Teichmüller theory; quasiconformal analysis

Domaines: Systèmes dynamiques [math.DS]

Matthieu Astorg. The Teichmüller space of a rational map immerses into moduli space. Advances in Mathematics, 2017, 313, pp.991-1023. ⟨10.1016/j.aim.2017.04.013⟩. ⟨hal-01002101v3⟩