Making some big assumptions -- ignoring possible singularities in spacetime, and assuming that spacetime has a spatial cross-section -- then the idea of a spatial universe might make sense. As long as it's locally 3-dimensional, then globally it would be what's called a 3-manifold (which is to 3 dimensions what a surface is to 2 dimensions). If further the universe is finite and without boundary, this would be a "compact" 3 manifold; if it's all in once piece, then it would even be "connected". Otherwise, it's just some 3-manifold. Taking your assumption of "uniform at large scales" to mean geometrically homogeneous, then the universe would be modeled on one of the 8 geometries in Bill Thurston's Geometrization conjecture, now apparently a theorem as proved by Grigori Perelman. If further the universe is geometrically isotropic, I think that would imply it has approximately constant (sectional) curvature. The 3-manifolds of constant positive curvature and constant 0 curvature have been fully classified. The 3-manifolds of constant negative curvature -- the "hyperbolic" ones -- are by any standard the most numerous among these three possibilities, and there are many books and papers devoted to them. --Dan --------------------------- Dave Dyer wrote: << I was thinking about a simulated 3-d map of the universe, based on Hubble deep field images, and it occurred to me that a 3-d map can't really be right, based on established cosmological models. If the universe is uniform at large scales, and we are not serindipitously located near the center, then the overall topology of the universe must be some strange non-intuitive thing. What are the possible maths of such a thing?
_____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele