Computing the Teichmüller Polynomial

Ferran Valdez

The Teichmüller polynomial of a fibered 3-manifold, introduced by McMullen at the end of the 90’s, plays a useful role in the construction of mapping classes with small entropy (small stretch factor). In this talk, we explain what this polynomial is and we provide an algorithm that computes the Teichmüller polynomial of the fibered face associated to a pseudo-Anosov mapping class of a disc homeomorphism. This algorithm is based on the results of Penner and Papadopoulos on train tracks (folding and splitting). This is joint work with Erwan Lanneau, from IF @ Grenoble.