Geometric & Functional Analysis GAFA

, Volume 7, Issue 3, pp 561–593

Structure and Rigidity in (Gromov) Hyperbolic Groups and Discrete Groups in Rank 1 Lie Groups II

DOI: 10.1007/s000390050019

Cite this article as:
Sela, Z. GAFA, Geom. funct. anal. (1997) 7: 561. doi:10.1007/s000390050019


We borrow the Jaco-Shalen-Johannson notion of characteristic sub-manifold from 3-dimensional topology to study cyclic splittings of torsion-free (Gromov) hyperbolic groups and finitely generated discrete groups in rank 1 Lie groups. Our JSJ canonical decomposition is a fundamental object for studying the dynamics of individual automorphisms and the automorphism group of a torsion-free hyperbolic group and a key tool in our approach to the isomorphism problem for these groups [S3]. For discrete groups in rank 1 Lie groups, the JSJ canonical decomposition serves as a basic object for understanding the geometry of the space of discrete faithful representations and allows a natural generalization of the Teichmüller modular group and the Riemann moduli space for these discrete groups.

Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • Z. Sela
    • 1
  1. 1.The Hebrew University, Jerusalem 91904, Israel IL
  2. 2.Columbia University, New York, NY 10027, USAUS

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