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

Ding, Fan; Wang, Shicheng; Yao, Jiangang

doi:10.1090/S0002-9947-08-04439-5

On embedding all $n$-manifolds into a single $(n+1)$-manifold
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by Fan Ding, Shicheng Wang and Jiangang Yao PDF

Trans. Amer. Math. Soc. 360 (2008), 6017-6030 Request permission

Abstract:

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 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.

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