  We construct the 'threshold manifold' near the soliton for the mass critical
gKdV equation, completing results obtained in arXiv:1204.4625 and
arXiv:1204.4624. In a neighborhood of the soliton, this C1 manifold of
codimension one separates solutions blowing up in finite time and solutions in
the 'exit regime'. On the manifold, solutions are global in time and converge
locally to a soliton. In particular, the soliton behavior is strongly unstable
by blowup.
