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Geometric & Functional Analysis GAFA

, Volume 7, Issue 3, pp 561–593 | Cite as

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

Abstract.

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.

Keywords

Automorphism Group Natural Generalization Discrete Group Basic Object Modular Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • Z. Sela
    • 1
  1. 1.The Hebrew University, Jerusalem 91904, Israel IL

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