# Do we expect that the universe is simply-connected? [duplicate]

I heard recently that the universe is expected to be essentially flat. If this is true, I believe this means (by the 3d Poincare conjecture) that the universe cannot be simply-connected, since the 3-sphere isn't flat (i.e. doesn't admit a flat metric).

Is any/all of this true? If so (or even if not), what sorts of unexpected things might follow from the non-simply-connectedness of our universe?

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## marked as duplicate by Michael Brown, Qmechanic♦May 2 '13 at 12:55

You seem to think the Poincare conjecture says that the 3-sphere is the only simply connected 3-manifold. By your logic $\mathbb{R^3}$ (which can be equipped with the flat metric) isn't simply connected. –  NikolajK May 2 '13 at 8:05