Structure and rigidity in hyperbolic groups I

@article{Rips1994StructureAR,
  title={Structure and rigidity in hyperbolic groups I},
  author={Eliyahu Rips and Zlil Sela},
  journal={Geometric \& Functional Analysis GAFA},
  year={1994},
  volume={4},
  pages={337-371}
}
  • 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. 
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93 Citations
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93 Citations

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References

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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.
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Free groups and graphs.- 2-Dimensional complexes and combinatorial presentations of groups.- Surfaces.- Planar discontinuous groups.- Automorphisms of planar groups.- On the complex analytic theory…
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LetFn.k be an orientable compact surface of genusn withk boundary components. For a suitable choice of 2n + 1 simple closed curves onFn,1 the corresponding Dehn twists generate bothMn,o andMn,1. A…
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© Publications mathématiques de l’I.H.É.S., 1992, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://…
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Degenerations of hyperbolic structures, III: Actions of 3-manifold groups on trees and Thurston’s compactness theorem
A finite set of generators for the homeotopy group of a 2-manifold
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