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

Fan Ding; Shicheng Wang; Jiangang Yao

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

Fan Ding·Shicheng Wang·Jiangang Yao

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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 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.

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BibTeX RIS

Fan Ding, Shicheng Wang, Jiangang Yao. 2005-09-24. On embedding all $n$-manifolds into a single $(n+1)$-manifold. https://arxiv.org/abs/math/0509579

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