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Embedding open 3-manifolds in compact 3-manifolds

Embedding open 3-manifolds in compact 3-manifolds

We consider open 3-maniίolds that are monotone unions of compact 3-manifolds each bounded by a torus.We give necessary and sufficient conditions for embedding such an open 3-manifold in a compact 3-manifold.We also show that if the open 3-manif old embeds in a compact 3-manif old, then it embeds in a …