Computing the Teichmüller polynomial

Abstract

The Teichmüller polynomial of a fibered 3-manifold, introduced in [McM00], plays a useful role in the construction of mapping classes having a small stretch factor. We provide a general algorithm for computing the Teichmüller polynomial given a pseudo-Anosov mapping class obtained as a loop in a train track automaton. As a byproduct, our algorithm allows us to derive all the relevant information on the topology of various fibers that belong to a fibered face.