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Conformal Geometry and Dynamics

ISSN 1088-4173



Properties of convergence groups and spaces

Author: Eric M. Freden
Journal: Conform. Geom. Dyn. 1 (1997), 13-23
MSC (1991): Primary 57S30; Secondary 20F38, 20F32
Published electronically: May 22, 1997
MathSciNet review: 1452414
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Abstract: This paper discusses algebraic and topological conditions that are consequences of a convergence group action.

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  • [B1] B. Bowditch, Convergence groups and configuration spaces, preprint, 1996.
  • [B2] -, A topological characterization of hyperbolic groups, preprint, 1996.
  • [B3] -, Geometrical finiteness for hyperbolic groups, J. Func. Anal. 113 (1993), 245-317. MR 94e:57016
  • [B4] -, Geometrical finiteness with variable negative curvature, Duke Math. J. 77 (1995), 229-274. MR 96b:53056
  • [C] J. Cannon, The Theory of Negatively Curved Spaces and Groups, Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces (T. Bedford, M. Keane, and C. Series, eds.), Oxford Univ. Press, 1991, pp. 315-369. CMP 92:02
  • [F] E. Freden, Negatively curved groups have the convergence property I, Ann. Acad. Sci. Fenn. 20 (1995), 333-348. MR 96g:20054
  • [GM1] F. Gehring, G. Martin, Discrete quasiconformal groups I, Proc. London Math. Soc. 55 (1987), 331-358. MR 88m:30057
  • [GM2] F. Gehring, G. Martin, Generalizations of Kleinian groups, MSRI preprint 06519-86, 1986.
  • [Gr] M. Gromov, Hyperbolic groups, in Essays in Group Theory, ed. S. M. Gersten, MSRI series 8 (1987), 75-263. MR 89e:20070
  • [K] R. Kulkarni, Groups with domains of discontinuity, Math. Ann. 237 (1978), 253-272. MR 81m:30046
  • [M] L. Mosher, Hyperbolic extensions of groups, Journal of Pure and Applied Algebra 110 (1996), 305-314. MR 97c:20056
  • [MKS] W. Magnus, A. Karrass, D. Solitar, Combinatorial Group Theory (second revised edition), Dover Publications, 1976. MR 54:10423
  • [MS] G. Martin, R. Skora, Group actions of the 2-sphere, Am. J. Math. 111 (1989), 387-402. MR 91e:57068
  • [N] P. Nicholls, The Ergodic Theory of Discrete Groups, London Mathematical Society Lecture Note Series 143, Cambridge University Press, 1989. MR 91i:58104
  • [S] Z. Sela, Endomorphisms of hyperbolic groups I: the Hopf property (to appear).
  • [SS] L. Steen, J. Seebach, Counterexamples in Topology, Dover Publications, 1995. MR 96k:54001
  • [T1] P. Tukia, Convergence groups and Gromov's metric hyperbolic spaces, New Zealand J. Math. 23 (1994), 157-187. MR 96c:30042
  • [T2] -, Conical limit points and uniform convergence groups, preprint, 1997.
  • [W] W. Woess, Fixed sets and free subgroups of groups acting on metric spaces, Math. Z. 214 (1993), 425-439. MR 94m:54093

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Additional Information

Eric M. Freden
Affiliation: Uintah Basin Education Center, 987 E. Lagoon St. (124-9), Roosevelt, Utah 84066

Received by editor(s): February 7, 1997
Published electronically: May 22, 1997
Article copyright: © Copyright 1997 American Mathematical Society

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