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

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

2005-09-24

arxiv.org/abs/math/0509579v1

Mathematics

Geometric Topology

21 pages, 3 figures

Scientific paper

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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