On a proof of the collapse conjecture for a diagonal Bianchi type-IX   vacuum space-time
  It is given a simple proof of the collapse conjecture for a diagonal Bianchi type-IX vacuum space-time. It is shown that the codimension of the infinity stable attractor, restricted to the anisotropy plane, is not zero, thus proving that "escape along a channel" is impossible. 
T. Charters
gr-qc math-ph math.MP