== Layman's statement ==
I made a couple tweaks to make this more accurate, and I hope I haven't compromised the accessibility too much:
:#Not sure what a "covering" means here, so I made it a statement about loops. But this is probably less clear. Any suggestions?:#The page made it sound like part of the conjecture is that S^3 is simply connected, but this is an easy fact. The hard part is that it's the ''only'' simply connected thing.:#The page made reference to "manifold in four-dimensional space". What we're really interested in is three-manifolds, and some of them don't even fit in four dimensional space, so this needs a tweak! A somewhat analogous example is the Klein bottle, a 2-dimensional manifold which doesn't fit in 3-dimensional space (without self-intersections). Thus I wrote "three dimensional space", with a link to [[manifold]].
I think my changes are not optimal, please continue to improve! --[[User:JimR|JimR]] 22:24, 22 December 2009 (EST)