Lacunary hyperbolic groups

  title={Lacunary hyperbolic groups},
  author={Mark V. Sapir},
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


Publications referenced by this paper.
Showing 1-10 of 34 references

et al

  • J. M. Alonso
  • Notes on word hyperbolic groups. Edited by H…
  • 1991
Highly Influential
10 Excerpts

On constricted and wide groups

  • C. Druţu, S. Mozes, M. Sapir
  • Preprint
  • 2006
Highly Influential
6 Excerpts


  • A. Yu
  • The Geometry of Defining Relations in Groups…
  • 1991
Highly Influential
9 Excerpts


  • Werner Ballmann. Lectures on spaces of nonpositive curvat Seminar
  • Birkhuser Verlag, Basel,
  • 1995
Highly Influential
2 Excerpts

to appear in Internat

  • A.Yu. Olshanskii, Groups with quadratic-non-quadratic Dehn functions
  • J. Algebra Comput.,
  • 2006

Tree-graded spaces and asymptotic cones of groups. With an appendix by Denis

  • C. Druţu, M. Sapir
  • Osin and Mark Sapir. Topology
  • 2005

A topological characterization of relatively hyperbolic groups

  • A. Yaman
  • J. Reine Angew. Math
  • 2004

Similar Papers

Loading similar papers…