Two-generator free Kleinian groups and hyperbolic displacements


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Yuce I. S.

ALGEBRAIC AND GEOMETRIC TOPOLOGY, cilt.14, sa.6, ss.3141-3184, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 6
  • Basım Tarihi: 2014
  • Doi Numarası: 10.2140/agt.2014.14.3141
  • Dergi Adı: ALGEBRAIC AND GEOMETRIC TOPOLOGY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.3141-3184
  • TED Üniversitesi Adresli: Evet

Özet

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.