Geometriae Dedicata

, Volume 180, Issue 1, pp 339–371

A Cartan–Hadamard type result for relatively hyperbolic groups

Original Paper Series A

DOI: 10.1007/s10711-015-0105-5

Cite this article as:
Coulon, R., Hull, M. & Kent, C. Geom Dedicata (2016) 180: 339. doi:10.1007/s10711-015-0105-5


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.


Relatively hyperbolic Asymptotic cones Tree-graded spaces 

Mathematics Subject Classification

20F65 20F67 20F69 

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.CNRS/IRMAR, Université de Rennes 1Rennes CedexFrance
  2. 2.Department of Mathematics, Statistics, and Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  3. 3.Courant Institute of MathematicsNew York UniversityNew YorkUSA

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