Relative free splitting and free factor complexes I: Hyperbolicity

2014/07/13 by Michael Handel, Lee Mosher, Handel, Michael +1 · 5 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.1407.3508

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 F_n, relative to the choice of a free factor system of F_n, 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 Γ, relative to the choice of a free factor system of Γ. 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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