Jon Perry writes: << ... I have developed a schema for characterizing ANY x-manifold, and in my scheme simply connected spaces fall into exactly one category, and hence are equivalent.
It really would be better if you devoted some effort toward making your posts comprehensible. Here you don't say what kind of "equivalent" you are talking about, so your assertion conveys zero information to anyone reading it. If you mean topologically equivalent, then this assertion is false, since (e.g.) each of the 4-manifolds S^4 and S^2 x S^2 is simply-connected but they are not homeomorphic. You also don't say what kind of manifolds you are considering (e.g., compact). If noncompact manifolds are covered by your assertion, then R^2 and S^2 provide a simpler counter-example of two simply-connected manifolds of ther same dimension that are non-homeomorphic. --Dan Asimov