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Original Articles

Free Subgroups of Groups with Nontrivial Floyd Boundary

Pages 5361-5376 | Received 01 Feb 2002, Published online: 31 Aug 2006

References

  • Bridson , M. R. and Haefliger , A. 1999 . Metric Spaces of Non-Positive Curvature , Grundlehren der Mathematischen Wissenchaften 319 Berlin : Springer-Verlag .
  • Floyd , W. J. 1980 . Group completions and limit sets of Kleinian groups . Invent. Math. , 57 : 205 – 218 .
  • Floyd , W. J. 1984 . Group completions and Furstenberg boundaries: Rank one . Duke Math. J. , 51 : 1017 – 1020 .
  • Freudenthal , H. 1931 . Über die Enden topologischer Räume und Gruppen . Math. Z. , 33 : 692 – 713 .
  • Freudenthal , H. 1942 . Neuaufbau der Endentheorie . Ann. of Math. , 43 : 261 – 279 .
  • Freudenthal , H. 1945 . Über die Enden diskrete Räume und Gruppen . Comment. Math. Helv. , 17 : 1 – 38 .
  • Furstenberg , H. Boundary theory and stochastic processes on homogeneous spaces . Proceedings of Symposia on Pure and Applied Math . 1972 , Williamstown, Mass. Harmonic Analysis on Homogeneous Spaces , Vol. 26 , pp. 193 – 229 .
  • Gehring , F. W. and Martin , G. J. 1987 . Discrete quasiconformal groups. I . Proc. London Math. Soc. , 55 ( 3 ) : 331 – 358 .
  • Gerasimov, V. (2002). Personal communication
  • Gromov , M. 1987 . “ Hyperbolic groups ” . In Essays in Group Theory Edited by: Gersten , S. 75 – 265 . MSRI Publication, Springer Verlag .
  • Gromov , M. 1993 . “ Asymptotic invariants of infinite groups ” . In Geometric Group Theory , London Math. Soc. LNS 182 Edited by: Niblo , G. A. and Roller , M. A. Vol. 2 , Cambridge University Press .
  • de la Harpe , P. 2000 . Topics in Geometric Group Theory , Chicago Lectures in Math. Chicago : University of Chicago Press .
  • Hopf , H. 1944 . Enden offener Räume und unendliche diskontinuerliche Gruppen . Comment. Math. Helv. , 16 : 81 – 100 .
  • Karlsson , A. 2001 . Non-expanding maps and Busemann functions . Ergod. Th. & Dynam. Sys. , 21 : 1447 – 1457 .
  • Karlsson, A. (2003). Boundaries and random walks on finitely generated infinite groups. To appear in Arkiv för Matematik
  • Karlsson , A. and Noskov , G. A. 2002a . The Hilbert metric and Gromov hyperbolicity . l'Enseign. Math. , 48 : 73 – 89 .
  • Karlsson, A., Noskov, G. A. (2002b). Some groups having only elementary actions on metric spaces with hyperbolic boundaries. Preprint of the FIM, ETH-Zürich
  • McMullen , C. T. 2001 . Local connectivity, Kleinian groups and geodesics on the blowup of the torus . Invent. Math. , 146 : 35 – 91 .
  • Stallings , J. R. 1968 . On torsion-free groups with infinitely many ends . Ann. of Math. , 88 ( 2 ) : 312 – 334 .
  • Stark , C. W. 1992 . Group completions and orbifolds of variable negative curvature . Proc. Amer. Math. Soc. , 114 : 191 – 194 .
  • Tits , J. 1972 . Free subgroups in linear groups . J. Algebra , 20 : 250 – 270 .
  • Tukia , P. 1988 . Holomorphic Functions and Moduli , A remark on a paper by Floyd (Berkeley, CA, 1986) Vol. II , 165 – 172 . Springer, New York : MSRI Publ. 11 .
  • Woess , W. 1993 . Fixed sets and free subgroups of groups acting on metric spaces . Math. Z. , 214 ( 3 ) : 425 – 439 .

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