So I've been under the impression for a while that cosmologists take the Poincare Conjecture to imply that the universe is topologically a 3-sphere. But I was reading my GR textbook and it says that Kerr black holes have a ring-shaped singularity. Wouldn't that mean that the universe isn't simply connected, because a loop running through a Kerr singularity wouldn't be able to be deformed to a point? And wouldn't that imply that the universe could be a torus or even a 3-surface of higher genus? Thanks for clearing this up.