  We construct a center-stable manifold of the ground state solitons in the
energy space for the critical wave equation without imposing any symmetry, as
the dynamical threshold between scattering and blow-up, and also as a
collection of solutions which stay close to the ground states. Up to energy
slightly above the ground state, this completes the 9-set classification of the
global dynamics in our previous paper. We can also extend the manifold to
arbitrary energy size by adding large radiation. The manifold contains all the
solutions scattering to the ground state solitons, and also some of those
blowing up in finite time by concentration of the ground states.
