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).
Mathieu Carette, Stefano Francaviglia, Ilya Kapovich, Armando Martino (2014). Corrigendum: “Spectral rigidity of automorphic orbits in free groups”. ALGEBRAIC AND GEOMETRIC TOPOLOGY, 14, 3081-3088 [10.2140/agt.2014.14.3081].
Corrigendum: “Spectral rigidity of automorphic orbits in free groups”
FRANCAVIGLIA, STEFANO;
2014
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
