Properties of convergence groups and spaces

Freden, Eric

doi:10.1090/S1088-4173-97-00011-8

Properties of convergence groups and spaces
HTML articles powered by AMS MathViewer

by Eric M. Freden

Conform. Geom. Dyn. 1 (1997), 13-23

DOI: https://doi.org/10.1090/S1088-4173-97-00011-8

Published electronically: May 22, 1997

PDF | Request permission

Abstract:

This paper discusses algebraic and topological conditions that are consequences of a convergence group action.

References

B. Bowditch, Convergence groups and configuration spaces, preprint, 1996.
—, A topological characterization of hyperbolic groups, preprint, 1996.
B. H. Bowditch, Geometrical finiteness for hyperbolic groups, J. Funct. Anal. 113 (1993), no. 2, 245–317. MR 1218098, DOI 10.1006/jfan.1993.1052
B. H. Bowditch, Geometrical finiteness with variable negative curvature, Duke Math. J. 77 (1995), no. 1, 229–274. MR 1317633, DOI 10.1215/S0012-7094-95-07709-6
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.
Eric M. Freden, Negatively curved groups have the convergence property. I, Ann. Acad. Sci. Fenn. Ser. A I Math. 20 (1995), no. 2, 333–348. MR 1346817
F. W. Gehring and G. J. Martin, Discrete quasiconformal groups. I, Proc. London Math. Soc. (3) 55 (1987), no. 2, 331–358. MR 896224, DOI 10.1093/plms/s3-55_{2}.331
F. Gehring, G. Martin, Generalizations of Kleinian groups, MSRI preprint 06519-86, 1986.
M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI 10.1007/978-1-4613-9586-7_{3}
R. S. Kulkarni, Groups with domains of discontinuity, Math. Ann. 237 (1978), no. 3, 253–272. MR 508756, DOI 10.1007/BF01420180
Lee Mosher, Hyperbolic extensions of groups, J. Pure Appl. Algebra 110 (1996), no. 3, 305–314. MR 1393118, DOI 10.1016/0022-4049(95)00081-X
Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory, Second revised edition, Dover Publications, Inc., New York, 1976. Presentations of groups in terms of generators and relations. MR 0422434
Gaven J. Martin and Richard K. Skora, Group actions of the $2$-sphere, Amer. J. Math. 111 (1989), no. 3, 387–402. MR 1002005, DOI 10.2307/2374665
Peter J. Nicholls, The ergodic theory of discrete groups, London Mathematical Society Lecture Note Series, vol. 143, Cambridge University Press, Cambridge, 1989. MR 1041575, DOI 10.1017/CBO9780511600678
Z. Sela, Endomorphisms of hyperbolic groups I: the Hopf property (to appear).
Lynn Arthur Steen and J. Arthur Seebach Jr., Counterexamples in topology, Dover Publications, Inc., Mineola, NY, 1995. Reprint of the second (1978) edition. MR 1382863
Pekka Tukia, Convergence groups and Gromov’s metric hyperbolic spaces, New Zealand J. Math. 23 (1994), no. 2, 157–187. MR 1313451
—, Conical limit points and uniform convergence groups, preprint, 1997.
Wolfgang Woess, Fixed sets and free subgroups of groups acting on metric spaces, Math. Z. 214 (1993), no. 3, 425–439. MR 1245204, DOI 10.1007/BF02572415