Re: [math-fun] The spatial universe is finite !!!???
John asks: << Is there a shape for space-time that makes space compact but that doesn't have an invariant factorization as space x time?
The lens spaces L(7,1) and L(7,2) (compact 3-manifolds) are known to be topologically distinct but homotopy equivalent. I wonder if L(7,1) x R is homeomorphic to L(7,2) x R. IF this is the case, then L(7,1) x R = L(7,2) x R is a topological 4-manifold with a non-unique factorization as (compact 3-manifold) x R. (Is this what you meant, John?) --Dan
On Sat, 11 Oct 2003 asimovd@aol.com wrote:
The lens spaces L(7,1) and L(7,2) (compact 3-manifolds) are known to be topologically distinct but homotopy equivalent. I wonder if
L(7,1) x R is homeomorphic to L(7,2) x R.
IF this is the case, then L(7,1) x R = L(7,2) x R is a topological 4-manifold with a non-unique factorization as (compact 3-manifold) x R.
(Is this what you meant, John?)
What I wanted was really a space-time that didn't factorize at all, rather than one for which the factorization wasn't unique. I don't believe, by the way, that the above two space-times are homeomorphic, but that's another matter. John Conway
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John Conway