NEGATIVELY CURVED GROUPS HAVE THE CONVERGENCE PROPERTY .1.

It is known that the Cayley graph Gamma of a negatively curved (Gromov-hyperbolic) group G has a well-defined boundary at infinity partial derivative Gamma. Furthermore, partial derivative Gamma is compact and metrizable. In this paper I show that G acts on partial derivative Gamma as a convergence group. This implies that if partial derivative Gamma similar or equal to S-1, then G is topologically conjugate to a cocompact Fuchsian group.