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.
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Submitted: September 1996, revised version: April 1997
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Sela, Z. Structure and Rigidity in (Gromov) Hyperbolic Groups and Discrete Groups in Rank 1 Lie Groups II. GAFA, Geom. funct. anal. 7, 561–593 (1997). https://doi.org/10.1007/s000390050019
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DOI: https://doi.org/10.1007/s000390050019