Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups II

Zlil Sela*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

109 Scopus citations


We borrow the Jaco-Shalen-Johannson notion of characteristic submanifold 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.

Original languageAmerican English
Pages (from-to)561-593
Number of pages33
JournalGeometric and Functional Analysis
Issue number3
StatePublished - 1997

Bibliographical note

Funding Information:
Partially supported by the Alon Fellowship, the Alfred P. Sloan Fellowship, and NSF Grant DMS-9402988.


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