On embedding all n-manifolds into a single (n+1)-manifold

摘要

For each composite number n not equal 2(k), there does not exist a single connected closed ( n + 1)-manifold such that any smooth, simply-connected, closed n-manifold can be topologically flatly embedded into it. There is a single connected closed 5-manifold W such that any simply-connected, 4-manifold M can be topologically flatly embedded into W if M is either closed and indefinite, or compact and with non-empty boundary.