Lacunary hyperbolic groups

@inproceedings{Sapir2007LacunaryHG,
  title={Lacunary hyperbolic groups},
  author={Mark V. Sapir},
  year={2007}
}
We call a finitely generated group lacunary hyperbolic if one of its asymptotic cones is an R-tree. We characterize lacunary hyperbolic groups as direct limits of Gromov hyperbolic groups satisfying certain restrictions on the hyperbolicity constants and injectivity radii. Using central extensions of lacunary hyperbolic groups, we solve a problem of Gromov by constructing a group whose asymptotic cone C has countable but non-trivial fundamental group (in fact C is homeomorphic to the direct… CONTINUE READING

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