The Second Bounded Cohomology of a Group Acting on a Gromov-Hyperbolic Space

Suppose a group G acts on a Gromov-hyperbolic space X properlydiscontinuously. If the limit set L(G) of the action has atleast three points, then the second bounded cohomology groupof is infinite dimensional. For example, if M is a complete, pinched negatively curved Riemannianmanifold with finite volume, then is infinite dimensional. As an application, we show that ifG is a knot group with GZ, then is infinite dimensional. 1991 Mathematics Subject Classification:primary 20F32; secondary 53C20, 57M25.