Exposed and denting points in duals of operator spaces

We study the extremal structure of the dual unit balls of various operator spaces. Mainly, we show that the classes of w*-] strongly exposed, w*-] exposed, and denting points in the dual unit balls of spaces of compact operators between Banach spacesX andY are completely — and in a canonical way — determined by the corresponding classes of points in the unit balls of the (bi-)duals of the factor spacesX andY. Applications to the duality of operator spaces and differentiability properties of the norm in operator spaces are given.