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

Ding, Fan; Wang, Shicheng; Yao, Jiangang

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

Authors

Ding, Fan

Wang, Shicheng

Yao, Jiangang

Description

For each composite number $n\ne 2^k$, there does not exist a single connected closed $(n+1)$-manifold such that any smooth, simply-connected, closed $n$-manifold can be topologically flat embedded into it. There is a single connected closed 5-manifold $W$ such that any simply-connected, 4-manifold $M$ can be topologically flat embedded into $W$ if $M$ is either closed and indefinite, or compact and with non-empty boundary.
21 pages, 3 figures