We show how to derive hyperbolicity of the free factor complex of FN from the Handel–Mosher proof of hyperbolicity of the free splitting complex of FN, thus obtaining an alternative proof of a theorem of Bestvina–Feighn. We also show that under the natural map τ from the free splitting complex to free factor complex, a geodesic [x,y] maps to a path that is uniformly Hausdorff-close to a geodesic [τ(x),τ(y)].
Classification :
20-XX
Mots-clés :
Free group, curve complex, outer automorphism group of the free group
Affiliations des auteurs :
Ilya Kapovich
1
;
Kasra Rafi
2
1
University of Illinois at Urbana-Champaign, USA
2
University of Oklahoma, Norman, USA
Ilya Kapovich; Kasra Rafi. On hyperbolicity of free splitting and free factor complexes. Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 391-414. doi: 10.4171/ggd/231
@article{10_4171_ggd_231,
author = {Ilya Kapovich and Kasra Rafi},
title = {On hyperbolicity of free splitting and free factor complexes},
journal = {Groups, geometry, and dynamics},
pages = {391--414},
year = {2014},
volume = {8},
number = {2},
doi = {10.4171/ggd/231},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/231/}
}
TY - JOUR
AU - Ilya Kapovich
AU - Kasra Rafi
TI - On hyperbolicity of free splitting and free factor complexes
JO - Groups, geometry, and dynamics
PY - 2014
SP - 391
EP - 414
VL - 8
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/231/
DO - 10.4171/ggd/231
ID - 10_4171_ggd_231
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%T On hyperbolicity of free splitting and free factor complexes
%J Groups, geometry, and dynamics
%D 2014
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%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/231/
%R 10.4171/ggd/231
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