Points with finite orbits for trace maps

Abstract

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

References in corpus (1)

• The SL(2,C) character variety of the one-holed torus