Abstract

We give a characterization of the geometric automorphisms in a certain class of free group automorphisms. When the automorphism is geometric, then it is induced by a pseudo-Anosov homeomorphism without interior singularities. An outer free group automorphism is given by a $1$-cocycle of a $2$-complex the fundamental group of which is the mapping-torus group of the automorphism. A combinatorial construction elucidates the link between this new representation and the classical representation of a free group automorphism by a graph-map [2]