Corrigendum to "Spectral rigidity of automorphic orbits in free groups"
(2014) Algebraic & Geometric Topology — (2014)
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- Abstract
- Lemma 5.1 in our paper [6] says that every infinite normal subgroup of Out(F_N) contains a fully irreducible element; this lemma was substantively used in the proof of the main result, Theorem A in [6]. Our proof of Lemma 5.1 in [6] relied on a subgroup classification result of Handel-Mosher [9], originally stated in [9] for arbitrary subgroups H≤Out(F_N). It subsequently turned out (see p. 1 in [10]) that the proof of the Handel-Mosher theorem needs the assumption that H be finitely generated. Here we provide an alternative proof of Lemma 5.1 from [6], which uses the corrected version of the Handel-Mosher theorem and relies on the 0-acylindricity of the action of Out(F_N) on the free factor complex (due to Bestvina-Mann-Reynolds).
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Carette, M., Francaviglia, S., Kapovich, I., & Martino, A. (2014). Corrigendum to “Spectral rigidity of automorphic orbits in free groups”. Algebraic & Geometric Topology. Accepted/in-press. https://hdl.handle.net/2078.5/200192 (Original work published 2014)