Topologically general U(1) symmetric Einstein spacetimes with AVTD   behavior
  We use Fuchsian methods to show that, for any two dimensional manifold $\Sigma^2$, there is a large family of U(1) symmetric solutions of the vacuum Einstein equations on the manifold $\Sigma \times S^1 \times \mathbb{R}$, each of which has AVTD behavior in the neighborhood of its singularity. 
Y. Choquet-Bruhat, J. Isenberg, and V. Moncrief