On hyperbolicity of free splitting and free factor complexes

By Ilya Kapovich, Kasra Rafi. 2012

80 citations recorded by the source corpus.

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 $[\tau(x),\tau(y)]$ .

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fb01ae198738ecfdb583c3ce1a05638cdff8c342

How researchers see this paper

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In Computational Theory and Mathematics

1. A. Hilion
2. Camille Horbez
3. O. Sarig

In Geometry and Topology

1. A. Hilion
2. Mariusz Urba'nski
3. David Simmons
4. Camille Horbez

In Mathematical Physics

1. A. Hilion
2. Mariusz Urba'nski
3. David Simmons
4. Camille Horbez
5. O. Sarig
6. V. Mayer

Citations in the corpus

• Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-proper Settings (2014, background): “In the process we came to realize that a more natural domain for our inquiries was the much larger setting of semigroups acting on Gromov hyperbolic metric spaces – that way we could simultaneously answer our own questions about H and construct a theoretical framework for those who are interested in”
• The hyperbolicity of the sphere complex via surgery paths (2012, methodology): “We recover the result [5] of Bestvina and Feighn on the hyperbolicity of the free factor complex, using an approach à la Kapovich and Rafi [18], as well as Masur and Schleimer’s result [22] on the hyperbolicity of the arc complex of a surface with boundary.”