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Corrigendum: “Spectral
rigidity of automorphic orbits in free groups”
Mathieu Carette, Stefano Francaviglia, Ilya Kapovich and Armando Martino |
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Algebraic & Geometric Topology 14 (2014) 3081–3088
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Abstract |
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Lemma 5.1 in our paper [CFKM] says that every infinite normal subgroup of 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 . It subsequently turned out (see Handel and Mosher page 1 of [HM1]) that the proof of the Handel-Mosher theorem needs the assumption that 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 –acylindricity of the action of 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 |
Keywords
free groups, spectral rigidity, geodesic currents
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Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 57M07, 37D40
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References |
Publication
Received: 1 November 2013
Revised: 19 November 2013
Accepted: 20 November 2013
Published: 5 November 2014
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Authors |
| Mathieu Carette | |
| Faculté des sciences Institut de recherche en mathématique et physique Chemin du Cyclotron 2 bte L7.01.01 1348 Louvain-la-Neuve Belgium |
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| Stefano Francaviglia | |
| Dipartimento di Matematica Università di Bologna Piazza di Porta San Donato 5 40126 Bologna Italy |
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| Ilya Kapovich | |
| Department of Mathematics University of Illinois at Urbana-Champaign 1409 West Green Street Urbana, IL 61801 USA |
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| Armando Martino | |
| School of Mathematics University of Southampton Highfield Southampton SO17 1BJ UK |
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