10 Oct
2003
10 Oct
'03
11:56 p.m.
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