It is possible for the topology to be non-trivial, but afaik we don’t know for sure; if the universe does loop back on itself, then it would be on large length scales that we can’t measure. We are fairly confident the universe is flat (has 0 curvature) at least. Note that this means that the universe probably doesn’t literally look like a donut: physical donuts have curvature, whereas topological tori need not have curvature. This is because a donut is a 2-torus embedded in 3D space, which isn’t equivalent to 2D space having the same topology as a 2-torus. A simple analogy for those who aren’t aware: an example of a 2D universe with non-trivial topology but flat geometry is a Pac-Man level, which is essentially a flat 2-torus. The curvature is flat everywhere, but it loops back on itself at the edges. Answer from cdstephens on reddit.com