- The hyperbolicity of the sphere complex via surgery paths arxiv link

Auteur(s): Hilion Arnaud, Horbez Camille

(Document sans référence bibliographique) 2012-10-23

Ref HAL: hal-00746622_v1
Ref Arxiv: 1210.6183
Ref. & Cit.: NASA ADS
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Handel and Mosher have proved that the free splitting complex FS for the free group is Gromov hyperbolic. This is a deep and much sought-after result, since it establishes FS as a good analogue of the curve complex for surfaces. We give a shorter alternative proof of this theorem, using surgery paths in Hatcher's sphere complex (another model for the free splitting complex), instead of Handel and Mosher's fold paths. As a byproduct, we get that surgery paths are unparameterized quasi-geodesics in the sphere complex.

Commentaires: 23 pages, 11 figures