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G^3 = Geometric Group Theory on the Gulf Coast Conference
February 5-8, 2004

Mobile, AL, USA

Organizers
Stephen Brick, Craig Jensen, Igor Mineyev

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The frequency space of a free group
by
Ilya Kapovich
University of Illinois at Urbana-Champaign

We analyze the structure of the frequency space of a free group Fk consisting of all shift-invariant Borel probability measures on the boundary of Fk and study the natural action of Out(Fk) on this frequency space. In particular we prove that for any outer automorphism f of Fk the conjugacy distortion spectrum of f, consisting of all numbers ||f(w)||/||w||, where w is a nontrivial conjugacy class, is a convex subset of the set of rational numbers. Other applications include a new algorithm for detecting hyperbolicity of an automorphism of Fk.

Paper reference: arXiv:math.GR/0311053

Date received: November 26, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # cami-03.