Structure and rigidity in hyperbolic groups I

  title={Structure and rigidity in hyperbolic groups I},
  author={Eliyahu Rips and Zlil Sela},
  journal={Geometric \& Functional Analysis GAFA},
  • E. Rips, Z. Sela
  • Published 1 May 1994
  • Mathematics
  • Geometric & Functional Analysis GAFA
We introduce certain classes of hyperbolic groups according to their possible actions on real trees. Using these classes and results from the theory of (small) group actions on real trees, we study the structure of hyperbolic groups and their automorphism group. 
Homogeneity of torsion-free hyperbolic groups
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Elementary embeddings in torsion-free hyperbolic groups
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The Hopf Property for Subgroups of Hyperbolic Groups
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Let be a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups. We construct Makanin–Razborov diagrams for . We also prove that every system of equations over is
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Test elements in torsion-free hyperbolic groups
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Stable actions of groups on real trees
This paper further develops Rips's work on real trees. We study a class of actions called ‘stable’ which includes actions with trivial arc stabilizers and small actions of hyperbolic groups.
Surfaces and Planar Discontinuous Groups
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Harmonic maps into singular spaces andp-adic superrigidity for lattices in groups of rank one
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