Points with finite orbits for trace maps

Abstract

We study an action of Aut(Fn) on R 2 n −1 by trace maps, defined using the traces of n-tuples of matrices in SL(2, C) having real traces. We determine the finite orbits for this action. These orbits essentially come from (i) the finite subgroups of SL(2, C), and (ii) a dense set of (rational) points in an embedded quotient of an n-torus.