The hyperbolicity of the sphere complex via surgery paths

Abstract : 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.
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Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2017, 730, pp.135-161. 〈10.1515/crelle-2014-0128〉
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https://hal.archives-ouvertes.fr/hal-00746622
Contributeur : Camille Horbez <>
Soumis le : lundi 29 octobre 2012 - 14:27:32
Dernière modification le : jeudi 15 novembre 2018 - 11:56:34

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Arnaud Hilion, Camille Horbez. The hyperbolicity of the sphere complex via surgery paths. Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2017, 730, pp.135-161. 〈10.1515/crelle-2014-0128〉. 〈hal-00746622〉

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