On the connectedness of the space of initial data for the einstein equations

Is the space of initial data for the Einstein vacuum equations connected? As a partial answer to this question, we prove the following result: Let M be the space of asymptotically at metrics of non-negative scalar curvature on ℝ³ which admit a global foliation outside a point by 2-spheres of positive mean and Gauss curvatures. Then M is connected.