The operation of drilling a tubular neighborhood of a knot in
and then gluing in a solid torus so that its meridian curve
goes to a -curve
on the torus boundary of the knot
exterior. Every compact connected 3-manifold comes from
Dehn surgery on a link in (Wallace 1960, Lickorish 1962).
Adams, C. C. "The Poincaré Conjecture, Dehn Surgery, and the Gordon-Luecke Theorem." §9.3 in The
Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.
New York: W. H. Freeman, pp. 257-263, 1994.Lickorish, W. B. R.
"A Representation of Orientable Combinatorial 3-Manifolds." Ann. Math.76,
531-540, 1962.Wallace, A. H. "Modifications and Cobounding
Manifolds." Canad. J. Math.12, 503-552, 1960.