an:01582742
Zbl 0973.20037
Swenson, Eric L.
Quasi-convex groups of isometries of negatively curved spaces
EN
Topology Appl. 110, No. 1, 119-129 (2001).
00073058
2001
j
20F67 57N10 57M07 57M60 53C23
quasiconvex subgroups; conical limit points; geometrically finite groups; Gromov hyperbolic metric spaces
\textit{B. H. Bowditch} has given the most careful analyses to date of the various possible definitions of geometrically finite groups [see J. Funct. Anal. 113, No. 2, 245-317 (1993; Zbl 0789.57007) and Duke Math. J. 77, No. 2, 229-274 (1995; Zbl 0877.57018)]. The author extends most of these results to Gromov hyperbolic metric spaces. Because of problems with finite generation, the author restricts himself to the case where there are no parabolic elements. He proves the equivalence of five conditions: the group is quasiconvex; all limit points are conical; all limit point are horospherical; the action is cocompact on the weak convex hull of the limit set; the action is cocompact on the union of the space and the domain of discontinuity at infinity.
J.W.Cannon (Provo)
Zbl 0789.57007; Zbl 0877.57018