Thurston theory old and new: decomposition of 3-manifolds and of surface automorphisms, and a new theorem in transcendental dynamics

We start by a panorama of closely related theorems by Thurston on geometrization of 3-manifolds, classification of surface automorphisms, and characterization of rational maps. These theorems are well known but often stated rather separately. We try to present them in a coherent way that highlights their close relations.

In the second part we will present a new theorem, in joint work with Sergey Shemyakov (AMU), that extends Thurston’s rational map theorem to a large class of transcendental functions; this responds to a conjecture raised by John Hubbard in the 1980’s.

This is joint work with Sergey Shemyakov.