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Hyperbolicity of the free splitting complex of F_n

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Lee Mosher (Rutgers)

Abstract: A free splitting of the rank n free group F_n is a minimal action of F_n on a nontrivial simplicial tree T with trivial edge stabilizers. Two free splittings are equivalent if the differ by an F_n-equivariant homeomorphism. The free splitting complex has a k-simplex for each equivalence class represented by a tree with k+1 orbits of natural edges (meaning edges with respect to the set of vertices of valence >=3). We prove that the free splitting complex is a Gromov hyperbolic metric space.