Dehn Surgery

The operation of drilling a tubular neighborhood of a knot K in S^3 and then gluing in a solid torus so that its meridian curve goes to a (p,q)-curve on the torus boundary of the knot exterior. Every compact connected 3-manifold comes from Dehn surgery on a link in S^3 (Wallace 1960, Lickorish 1962).

See also

Kirby Calculus, Tubular Neighborhood

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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.

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Dehn Surgery

Cite this as:

Weisstein, Eric W. "Dehn Surgery." From MathWorld--A Wolfram Web Resource.

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