Geodesic Currents and Length Compactness for Automorphisms of Free Groups
نویسنده
چکیده
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.
منابع مشابه
Hyperbolic structures on surfaces and geodesic currents
These are lecture notes for a course given by the authors during the program Automorphisms of Free Groups: Geometry, Topology, and Dynamics, held at the CRM (Barcelona) in 2012. The main objective of the notes is to describe Bonahon’s construction of Thurston’s compactification of Teichmüller space, in terms of geodesic currents on surfaces. In the final section, we present several extensions o...
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