Freden, Eric M. Negatively curved groups have the convergence property. I. (English) Zbl 0847.20031 Ann. Acad. Sci. Fenn., Ser. A I, Math. 20, No. 2, 333-348 (1995). 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. Reviewer: E.M.Freden (Provo) Cited in 1 ReviewCited in 19 Documents MSC: 20F65 Geometric group theory 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms Keywords:negatively curved groups; Gromov hyperbolic groups; Cayley graphs; convergence groups; cocompact Fuchsian groups PDFBibTeX XMLCite \textit{E. M. Freden}, Ann. Acad. Sci. Fenn., Ser. A I, Math. 20, No. 2, 333--348 (1995; Zbl 0847.20031) Full Text: EuDML EMIS