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

Mathieu Carette, Stefano Francaviglia, Ilya Kapovich and Armando Martino

Algebraic & Geometric Topology 14 (2014) 3081–3088

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

free groups, spectral rigidity, geodesic currents
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 57M07, 37D40
Received: 1 November 2013
Revised: 19 November 2013
Accepted: 20 November 2013
Published: 5 November 2014
Mathieu Carette
Faculté des sciences
Institut de recherche en mathématique et physique
Chemin du Cyclotron 2 bte L7.01.01
1348 Louvain-la-Neuve
Stefano Francaviglia
Dipartimento di Matematica
Università di Bologna
Piazza di Porta San Donato 5
40126 Bologna
Ilya Kapovich
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 West Green Street
Urbana, IL 61801
Armando Martino
School of Mathematics
University of Southampton
Southampton SO17 1BJ