The free splitting complex of a free group, I Hyperbolicity

Handel, Michael¹ ; Mosher, Lee²

¹ Mathematics & Computer Science Department, Herbert H Lehman College (CUNY), Bronx, NY 10468-1589, USA
² Department of Mathematics and Computer Science, Rutgers University, Newark, Newark, NJ 07102, USA

Geometry & topology, Tome 17 (2013) no. 3, pp. 1581-1670.

Résumé

We prove that the free splitting complex of a finite rank free group, also known as Hatcher’s sphere complex, is hyperbolic.

Détail

DOI : 10.2140/gt.2013.17.1581

Classification : 20F65, 57M07
Keywords: free splitting complex, outer automorphism group of a free group

Bibliographie

[1] J Aramayona, J Souto, Automorphisms of the graph of free splittings, Michigan Math. J. 60 (2011) 483

[2] M Bestvina, M Feighn, Hyperbolicity of the complex of free factors

[3] M Bestvina, M Feighn, Bounding the complexity of simplicial group actions on trees, Invent. Math. 103 (1991) 449

[4] M Bestvina, M Feighn, M Handel, Laminations, trees, and irreducible automorphisms of free groups, Geom. Funct. Anal. 7 (1997) 215

[5] M Bestvina, M Feighn, M Handel, The Tits alternative for Out(Fn), I : Dynamics of exponentially-growing automorphisms, Ann. of Math. 151 (2000) 517

[6] M Culler, J W Morgan, Group actions on R–trees, Proc. London Math. Soc. 55 (1987) 571

[7] V Guirardel, G Levitt, JSJ decompositions: Definitions, existence, uniqueness, II: Compatibility and acylindricity

[8] M Handel, L Mosher, Lipschitz retraction and distortion for subgroups of Out(Fn), Geom. Topol. 17 (2013) 1535

[9] A Hatcher, Homological stability for automorphism groups of free groups, Comment. Math. Helv. 70 (1995) 39

[10] A Hatcher, K Vogtmann, The complex of free factors of a free group, Quart. J. Math. Oxford Ser. 49 (1998) 459

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

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

[13] B Mann, Hyperbolicity of the cyclic splitting complex

[14] J F Manning, Geometry of pseudocharacters, Geom. Topol. 9 (2005) 1147

[15] H Masur, Y Minsky, Geometry of the complex of curves, I : Hyperbolicity, Invent. Math. 138 (1999) 103

[16] H Masur, L Mosher, S Schleimer, On train-track splitting sequences, Duke Math. J. 161 (2012) 1613

[17] L Sabalka, D Savchuk, On the geometry of the edge splitting complex, to appear in Groups, Geometry, and Dynamics (2013)

[18] S Schleimer, Notes on the complex of curves (2006)

[19] P Scott, T Wall, Topological methods in group theory, from: "Homological group theory" (editor T Wall), London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 137

[20] J R Stallings, Topology of finite graphs, Invent. Math. 71 (1983) 551