Atlas: Hyperbolic automorphisms of torsion-free hyperbolic groups by Peter Brinkmann

Atlas home || Conferences | Abstracts | about Atlas

G^3 = Geometric Groups on the Gulf coast
May 28-29, 1999
University of South Alabama
Mobile, AL, USA

Organizers
Phil Bowers, Stephen Brick, Jon Corson

Hyperbolic automorphisms of torsion-free hyperbolic groups
by
Peter Brinkmann
University of Utah

Let G be a torsion-free hyperbolic group. An automorphism \phi:G --> G is said to be hyperbolic if there exist numbers M > 0 and \lambda > 1 such that

\lambda·|g| <= max
{ |\phi^M(g)|, |\phi^-M(g)| }

for all g in G, where |.| denotes some word metric on G. This condition is invariant under quasi-isometries, so the choice of |.| does not matter.

We will show that an automorphism \phi:G --> G is hyperbolic if it has no nontrivial periodic conjugacy classes. The proof uses Sela's work on JSJ decompositions as well as an extension of the train track technique of Bestvina, Feighn and Handel.

http://www.math.utah.edu/~brinkman/

Date received: May 21, 1999