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).
Dehn Surgery
See also
Kirby Calculus, Tubular NeighborhoodExplore with Wolfram|Alpha
References
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.Referenced on Wolfram|Alpha
Dehn SurgeryCite this as:
Weisstein, Eric W. "Dehn Surgery." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DehnSurgery.html