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, the manifold drilled along is obtained by removing an open tubular neighborhood of from . If , the drilled manifold has torus boundary components . The manifold drilled along is also known as the link complement, since if one removed the corresponding closed tubular neighborhood from , one obtains a manifold diffeomorphic to .
* Given a 3-manifold whose boundary is made of 2-tori , we may glue in one solid torus

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