Geodesic currents and length compactness for automorphisms of free groups

Details Geodesic currents and length compactness for automorphisms of free groups Geodesic currents and length compactness for automorphisms of free groups

2006-02-24

arxiv.org/abs/math/0602555v2

Trans. of AMS 361(1) 2009, 161-176

Mathematics

Group Theory

Changes from v1: the proof of main theorem is a little different; added a section with generalisations. This is the version ac

Scientific paper

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.

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