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

Carette, Mathieu¹ ; Francaviglia, Stefano² ; Kapovich, Ilya³ ; Martino, Armando⁴

¹Faculté des sciences, Institut de recherche en mathématique et physique, Chemin du Cyclotron 2 bte L7.01.01, 1348 Louvain-la-Neuve, Belgium
²Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, 40126 Bologna, Italy
³Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801, USA
⁴School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, UK

Algebraic and Geometric Topology, Tome 14 (2014) no. 5, pp. 3081-3088

Résumé

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

Détail

DOI : 10.2140/agt.2014.14.3081

Classification : 20F65, 57M07, 37D40
Keywords: free groups, spectral rigidity, geodesic currents

Bibliographie

[1] M Bestvina, M Feighn, Outer limits, preprint (1993)

[2] M Bestvina, M Feighn, A hyperbolic $\mathrm{Out}(F^n)$–complex, Groups Geom. Dyn. 4 (2010) 31

[3] M Bestvina, M Feighn, Hyperbolicity of the complex of free factors, Adv. Math. 256 (2014) 104

[4] M Bestvina, P Reynolds, The boundary of the complex of free factors,

[5] M Carette, S Francaviglia, I Kapovich, A Martino, Spectral rigidity of automorphic orbits in free groups, Algebr. Geom. Topol. 12 (2012) 1457

[6] T Coulbois, A Hilion, M Lustig, $\mathbb R$–trees and laminations for free groups, II: The dual lamination of an $\mathbb R$–tree, J. Lond. Math. Soc. 78 (2008) 737

[7] F Dahmani, V Guirardel, D Osin, Hyperbolically embedded subgroups and rotating families in groups acting on hyperbolic spaces,

[8] M Handel, L Mosher, Subgroup classification in $\mathrm{Out}(F^n)$,

[9] M Handel, L Mosher, Subgroup decomposition in $\mathrm{Out}(F^n)$: Introduction and research announcement,

[10] A Hilion, C Horbez, The hyperbolicity of the sphere complex via surgery paths,

[11] I Kapovich, Currents on free groups, from: "Topological and asymptotic aspects of group theory" (editors R Grigorchuk, M Mihalik, M Sapir, Z Šunik), Contemp. Math. 394, Amer. Math. Soc. (2006) 149

[12] I Kapovich, M Lustig, Geometric intersection number and analogues of the curve complex for free groups, Geom. Topol. 13 (2009) 1805

[13] I Kapovich, M Lustig, Intersection form, laminations and currents on free groups, Geom. Funct. Anal. 19 (2010) 1426

[14] I Kapovich, A Myasnikov, Stallings foldings and subgroups of free groups, J. Algebra 248 (2002) 608

[15] I Kapovich, K Rafi, On hyperbolicity of free splitting and free factor complexes,

[16] D Osin, Acylindrically hyperbolic groups,

[17] P Reynolds, Reducing systems for very small trees,

[18] S C Wang, B Zimmermann, The maximum order of finite groups of outer automorphisms of free groups, Math. Z. 216 (1994) 83