an:00902742
Zbl 0847.20031
Freden, Eric M.
Negatively curved groups have the convergence property. I
EN
Ann. Acad. Sci. Fenn., Ser. A I, Math. 20, No. 2, 333-348 (1995).
00034640
1995
j
20F65 57S05
negatively curved groups; Gromov hyperbolic groups; Cayley graphs; convergence groups; cocompact Fuchsian groups
It is known that the Cayley graph \(\Gamma\) of a negatively curved (Gromov-hyperbolic) group \(G\) has a well-defined boundary at infinity \(\partial\Gamma\). Furthermore, \(\partial\Gamma\) is compact and metrizable. In this paper it is shown that \(G\) acts on \(\partial\Gamma\) as a convergence group. This implies that if \(\partial\Gamma\simeq\partial\Gamma{\mathbf S}^1\), then \(G\) is topologically conjugate to a cocompact Fuchsian group.
E.M.Freden (Provo)