Abstract
Pseudo-Anosov homeomorphisms are classified by their invariant train tracks. The
decomposition of any train track map in elementary folding maps gives a normal form for
each train track class. In the case of 4-braids there are three train tracks
classes and we give an explicit automaton that generates a normal form for each class.
This enables us, for instance, to exhibit the pseudo-Anosov 4-braid with the
minimal growth rate. We also show that the growth rate of a pseudo-Anosov braid
appears as a root of the Alexander polynomial of a link that shares a common
sub-link with the closure of the braid. We finally give a criterion for the
faithfulness of the Burau representation for 4-braids.