Relative free splitting and free factor complexes I: Hyperbolicity
Abstract
We study the large scale geometry of the relative free splitting complex and the relative free factor complex of the rank n free group Fn, relative to the choice of a free factor system of Fn, proving that these complexes are hyperbolic. Furthermore we present the proof in a general context, obtaining hyperbolicity of the relative free splitting complex and of the relative free factor complex of a general group , relative to the choice of a free factor system of . The proof yields information about coarsely transitive families of quasigeodesics in each of these complexes, expressed in terms of fold paths of free splittings.
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