Computing the Teichmüller polynomial

The Teichmüller polynomial of a fibered 3-manifold 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 and elementary operations on them (folding and splitting). This is joint work with Erwan Lanneau.

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