Two-generator free Kleinian groups and hyperbolic displacements

Creative Commons License

Yuce I. S.

ALGEBRAIC AND GEOMETRIC TOPOLOGY, vol.14, no.6, pp.3141-3184, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 6
  • Publication Date: 2014
  • Doi Number: 10.2140/agt.2014.14.3141
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3141-3184
  • TED University Affiliated: Yes


The log 3 theorem, proved by Culler and Shalen, states that every point in the hyperbolic 3-space H-3 is moved a distance at least log 3 by one of the noncommuting isometries xi or eta of H-3 provided that xi and eta generate a torsion-free, discrete group which is not cocompact and contains no parabolic. This theorem lies in the foundations of many techniques that provide lower estimates for the volumes of orientable, closed hyperbolic 3-manifolds whose fundamental groups have no 2-generator subgroup of finite index and, as a consequence, gives insights into the topological properties of these manifolds.