Shape of the universe

What is the 3-manifold of comoving space, i.e., of a comoving spatial section of the universe, informally called the "shape" of the universe? Neither the curvature nor the topology is presently known, though the curvature is known to be "close" to zero on observable scales. Is the shape unmeasurable; the Poincaré space; or another 3-manifold?

Open the “Cosmology and general relativity” section on Wikipedia →

Source: List of unsolved problems in physics (CC BY-SA 4.0)