We prove a compactness theorem for automorphisms of free groups. Namely, we show that the set of automorphisms keeping the length of the uniform current bounded is compact (up to conjugation). This implies that the spectrum of the length of the images of the uniform current is discrete, proving a conjecture of I. Kapovich. © 2008 American Mathematical Society.
|Journal||Transactions of the American Mathematical Society|
|Publication status||Published - 1 Jan 2009|
- Free groups
- Geodesic currents