# Bonn Topology Group - Abstracts

### Talk

MARTIN LUSTIG (Marseille): Fixed currents for hyperbolic automorphisms of free groups (07/01/2014)

### Abstract

It is known that for an irreducible hyperbolic automorphisms \phi of a finitely generated non-abelian free group F_n there are precisely two currents \mu_+ and \mu_- which are projectively fixed, i.e. \phi(\mu_+) = \lambda_+ \mu_+ and \phi(\mu_-) = \lambda_- \mu_-, for some positive "stretching factors" \lambda_+ > 1 and \lambda_- < 1.

In this talk we will explain how to generalize this result to general hyperbolic automorphisms \psi of F_n, and exhibit a natural bijection from the set of projectively fixed currents to the set of non-negative (row) eigenvectors for the transition matrix of a train track representative of \psi or of \psi^{-1}.

We will also apply this result to exhibit the first known example of any R-tree T in compactified Outer space which is not "diagonally equalizable".

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