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arXiv · 1611.02743

Points with finite orbits for trace maps

Stephen Humphries
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Abstract

We study an action of ${\rm Aut}(F_n)$ 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.

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Stephen Humphries. 2016-11-08. Points with finite orbits for trace maps. https://arxiv.org/abs/1611.02743

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