Corrigendum: “Spectral rigidity of automorphic orbits in free groups”

Abstract

Lemma 5.1 in our paper [CFKM] says that every infinite normal subgroup of $Out\left(F_N\right)$ contains a fully irreducible element; this lemma was substantively used in the proof of the main result, Theorem A in [CFKM]. Our proof of Lemma 5.1 in [CFKM] relied on a subgroup classification result of Handel and Mosher [HM], originally stated in [HM] for arbitrary subgroups $H\le Out\left(F_N\right)$. It subsequently turned out (see Handel and Mosher page 1 of [HM1]) that the proof of the Handel-Mosher theorem needs the assumption that $H$ is finitely generated. Here we provide an alternative proof of Lemma 5.1 from [CFKM], which uses the corrected version of the Handel-Mosher theorem and relies on the $0$–acylindricity of the action of $Out\left(F_N\right)$ on the free factor complex (due to Bestvina, Mann and Reynolds).

[CFKM]: Algebr. Geom. Topol. 12 (2012) 1457–1486 [HM]: arxiv:0908.1255 [HM1]: arxiv:1302.2681