A Cartan–Hadamard type result for relatively hyperbolic groups
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- Coulon, R., Hull, M. & Kent, C. Geom Dedicata (2016) 180: 339. doi:10.1007/s10711-015-0105-5
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In this article, we prove that if a finitely presented group has an asymptotic cone which is tree-graded with respect to a precise set of pieces then it is relatively hyperbolic. This answers a question of Mark Sapir and generalizes a result of Kapovich and Kleiner to relatively hyperbolic groups.