Topologically general U(1) symmetric Einstein spacetimes with AVTD behavior

We use Fuchsian methods to show that, for any two dimensional manifold $Σ^2$, there is a large family of U(1) symmetric solutions of the vacuum Einstein equations on the manifold $Σ\times S^1 \times \mathbb{R}$, each of which has AVTD behavior in the neighborhood of its singularity.

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