- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:00
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
8
2014
2
On hyperbolicity of free splitting and free factor complexes
Ilya
Kapovich
University of Illinois at Urbana-Champaign, URBANA, UNITED STATES
Kasra
Rafi
University of Oklahoma, NORMAN, UNITED STATES
Free group, curve complex, outer automorphism group of the free group
We show how to derive hyperbolicity of the free factor complex of $F_N$ from the Handel–Mosher proof of hyperbolicity of the free splitting complex of $F_N$, thus obtaining an alternative proof of a theorem of Bestvina–Feighn. We also show that under the natural map $\tau$ 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 $[\tau(x),\tau(y)]$.
Group theory and generalizations
391
414
10.4171/GGD/231
http://www.ems-ph.org/doi/10.4171/GGD/231