This paper addresses the dexterous manipulation planning problem, which deals with motion planning for a multi-fingered hand manipulating objects among static obstacles, under quasi-static movement assumption. We propose a general manipulation approach able to compute object and finger trajectories, as well as the finger relocation sequence, in order to link any two given configurations of the composite system hand + object. It relies on a topological property that characterizes the existence of solutions in the subspace of configurations where the object is grasped by the n fingers. This property helps reduce the problem by structuring the search space. The developed planner captures in a probabilistic roadmap the connectivity of submanifolds of the composite configuration space. The answer to the manipulation planning query is then given by searching a path in the computed graph. Simulation experiments are reported for different multi-fingered manipulation task examples showing the efficiency of the proposed method.