A Combination Theorem for Strong Relative Hyperbolicity

Abstract

We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic groups and answers a question of Swarup. We also prove a converse to the main Combination Theorem.

v2: 19 pages, no figures. Slight typographical differences with published version. Converse to main combination theorem added

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• Complex of Relatively Hyperbolic Groups
• Height in Splitting of Relatively Hyperbolic Groups
• Combination Theorems in Groups, Geometry and Dynamics
• Cubulating a free-product-by-cyclic group
• Cubulating Drilled bundles over graphs
• Geometry of extensions of free groups via automorphisms with fixed points on the complex of free factors