References
[AN]Adeleke, S. A. &Neumann, P. M.,Relations Related to Betweenness: Their Structure and Automorphisms. Mem. Amer. Math. Soc., 623. Amer. Math. Soc., Providence, RI, 1998.
[BM]Bestvina, M. &Mess, G., The boundary of negatively curved groups.J. Amer. Math. Soc., 4 (1991), 469–481.
[Bo1]Bowditch, B. H.,Treelike Structures Arising from Continua and Convergence Groups. To appear in Mem. Amer. Math. Soc.
[Bo2]Bowditch, B. H., Group actions on trees and dendrons. To appear inTopology.
[Bo3]Bowditch, B. H., Boundaries of strongly accessible hyperbolic groups. Preprint, Melbourne, 1996.
[Bo4]Bowditch, B. H., Convergence groups and configuration spaces. To appear inGroup Theory Down Under (J. Cossey, C. F. Miller, W. D. Neumann and M. Shapiro, eds.), de Gruyter.
[Bo5]Bowditch, B. H., Connectedness properties of limit sets. To appear inTrans. Amer. Math. Soc.
[Bo6]Bowditch, B. H., A topological characterisation of hyperbolic groups. To appear inJ. Amer. Math. Soc.
[CJ]Casson, A. &Jungreis, D., Convergence groups and Seifert fibered 3-manifolds.Invent. Math., 118 (1994), 441–456.
[DD]Dicks, W. &Dunwoody, M. J.,Groups Acting on Graphs. Cambridge Stud. Adv. Math., 17. Cambridge Univ. Press, Cambridge-New York, 1989.
[DP]Delzant, T. &Potyagailo, L., Accessibilité hiérarchique des groupes de présentation finie. Preprint, Strasbourg/Lille, 1998.
[DSa]Dunwoody, M. J. & Sageev, M. E., JSJ-splittings for finitely presented groups over slender subgroups. To appear inInvent. Math.
[DSw]Dunwoody, M. J. & Swenson, E. L. The algebraic annulus theorem. Preprint, Southampton, 1996.
[Du]Dunwoody, M. J., The accessibility of finitely presented groups.Invent. Math., 81 (1985), 449–457.
[FP]Fujiwara, K. & Papasoglu, P., JSJ decompositions of finitely presented groups and complexes of groups. Preprint, 1997.
[Fr]Freden, E. M., Negatively curved groups have the convergence property.Ann. Acad. Sci. Fenn. Ser. A I Math., 20 (1995), 333–348.
[Ga]Gabai, D., Convergence groups are Fuchsian groups.Ann. of Math., 136 (1992), 447–510.
[GH]Ghys, E. &Harpe, P. de la,Sur les groupes hyperboliques d'après Mikhael Gromov. Progr. Math., 83. Birkhäuser, Boston, MA, 1990.
[GM1]Gehring, F. W. &Martin, G. J., Discrete quasiconformal groups, I.Proc. London Math. Soc., 55 (1987), 331–358.
[GM2]Gehring, F. W. & Martin, G. J., Discrete quasiconformal groups, II. Handwritten notes.
[Gr]Gromov, M., Hyperbolic groups, inEssays in Group Theory (S. M. Gersten, ed.), pp. 75–263. Math. Sci. Res. Inst. Publ., 8. Springer-Verlag, New York-Berlin, 1987.
[Gu]Guralnik, D. P., Constructing a splitting-tree for a cusp-finite group acting on a Peano continuum (Hebrew). M.Sc. Dissertation, Technion, Haifa, 1998.
[HY]Hocking, J. G. &Young, G. S.,Topology. Addison-Wesley, Reading, MA, 1961.
[Jo]Johannson, K.,Homotopy Equivalences of 3-Manifolds with Boundaries. Lecture Notes in Math., 761. Springer-Verlag, Berlin-New York, 1979.
[JS]Jaco, W. H. &Shalen, P. B.,Seifert Fibered Spaces in 3-Manifolds. Mem. Amer. Math. Soc., 220. Amer. Math. Soc., Providence, RI, 1979.
[K]Kropholler, P. H., A group-theoretic proof of the torus theorem, inGeometric Group Theory, Vol. 1 (Sussex, 1991), pp. 138–158. London Math. Soc. Lecture Note Ser., 181. Cambridge Univ. Press, Cambridge, 1993.
[L]Levitt, G., Non-nesting actions on real trees.Bull. London Math. Soc., 30 (1998), 46–54.
[MNS]Miller III, C. F., Neumann, W. D. & Swarup, G. A., Some examples of hyperbolic groups. To appear inGroup Theory Down Under (J. Cossey, C. F. Miller, W. D. Neumann and M. Shapiro, eds.), de Gruyter.
[P]Paulin, F., Outer automorphisms of hyperbolic groups and small actions onR-trees, inArboreal Group Theory (Berkeley, CA, 1988), pp. 331–343. Math. Sci. Res. Inst. Publ., 19. Springer-Verlag, New York, 1991.
[RS]Rips, E. &Sela, Z., Cyclic splittings of finitely presented groups and the canonical JSJ decomposition.Ann. of Math., 146 (1997), 53–109.
[Se]Sela, Z., Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank 1 Lie groups, II.Geom. Funct. Anal., 7 (1997), 561–593.
[Sha]Shalen, P. B., Dendrology and its applications, inGroup Theory from a Geometrical Viewpoint (Trieste, 1990), pp. 543–616. World Sci. Publishing, River Edge, NJ, 1991.
[Sho]Short, H., Quasiconvexity and a theorem of Howson's, inGroup Theory from a Geometrical Viewpoint (Trieste, 1990), pp. 168–176. World Sci. Publishing, River Edge, NJ, 1991.
[SS]Scott, P. & Swarup, G. A., An algebraic annulus theorem. Preprint.
[St]Stallings, J. R.,Group Theory and Three-Dimensional Manifolds. Yale Math. Monographs, 4. Yale Univ. Press, New Haven, 1971.
[Sw]Swarup, G. A., On the cut point conjecture.Electron. Res. Announc. Amer. Math. Soc., 2 (1996), 98–100 (electronic).
[T1]Tukia, P., Homeomorphic conjugates of Fuchsian groups.J. Reine Angew. Math., 391 (1988), 1–54.
[T2] —, Convergence groups and Gromov's metric hyperbolic spaces.New Zealand J. Math., 23 (1994), 157–187.
[W]Ward, L. E., Axioms for cutpoints, inGeneral Topology and Modern Analysis (Univ. of California, Riverside, CA, 1980), pp. 327–336. Academic Press, New York-London, 1981.
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Bowditch, B.H. Cut points and canonical splittings of hyperbolic groups. Acta Math. 180, 145–186 (1998). https://doi.org/10.1007/BF02392898
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DOI: https://doi.org/10.1007/BF02392898