Geodesic currents and length compactness for automorphisms of free groups
arXiv:math/0602555
Abstract
We prove a compactness theorem for automorphisms of free groups. Namely, we show that the set of automorphisms keeping bounded the length of the uniform current is compact (up to conjugation.) This implies that the spectrum of the length of the images of the uniform current is discrete, answering to a conjecture of I. Kapovich.
Changes from v1: the proof of main theorem is a little different; added a section with generalisations. This is the version accepted for pubblication