## Algebraic & Geometric Topology

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

#### Abstract

Lemma 5.1 in our paper [CFKM] says that every infinite normal subgroup of $Out(FN)$ 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 $H≤ Out(FN)$. 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 $Out(FN)$ 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

#### Article information

Source
Algebr. Geom. Topol., Volume 14, Number 5 (2014), 3081-3088.

Dates
Revised: 19 November 2013
Accepted: 20 November 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513716010

Digital Object Identifier
doi:10.2140/agt.2014.14.3081

Mathematical Reviews number (MathSciNet)
MR3276855

Zentralblatt MATH identifier
1307.20037

#### Citation

Carette, Mathieu; Francaviglia, Stefano; Kapovich, Ilya; Martino, Armando. Corrigendum: “Spectral rigidity of automorphic orbits in free groups”. Algebr. Geom. Topol. 14 (2014), no. 5, 3081--3088. doi:10.2140/agt.2014.14.3081. https://projecteuclid.org/euclid.agt/1513716010

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