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  "body": "\n## Summary\n\nDehn surgery builds a new [[3-manifold|R20TB2KEQQ]] from a [[knot|QYEAZTYGPT]] or [[link|1A5WRCNTM3]] in a given one.\nOne removes a solid torus around the knot.\nThen one glues it back so that its meridian disc caps off a chosen curve on the boundary torus.\nFor knots in $S^3$ the choices are labelled by a number $p/q \\in \\Q \\cup \\set{\\infty}$.\nBy the [[Lickorish–Wallace theorem|1YP4RF1QXV]], every closed orientable $3$-manifold arises by Dehn surgery on a link in $S^3$.\n\n## Explanations\n\n### L1 human\n\nThink of a knotted rope inside space, wrapped in a thin solid tube.\nRemove the tube and put a solid tube back in, but twisted.\nNow the disc that used to go around the rope closes off a different loop on the tube's surface.\nThe space you get may be completely new.\nFor the simplest knot, the round circle, surgery with label $0$ gives the product of a sphere and a circle.\n",
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