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  "body": "\n## Summary\n\nKirby calculus is a set of moves on framed link diagrams in the $3$-sphere that relate any two diagrams describing the same $3$-manifold.\nA framed [[link|1A5WRCNTM3]] describes a $4$-manifold, obtained by attaching $2$-handles to the $4$-ball along the link, and its boundary $3$-manifold, obtained by [[Dehn surgery|ZA405B0Z1S]].\nRobion Kirby proved that two framed links give the same oriented $3$-manifold if and only if they are related by his moves.\nIt is a basic working tool of $3$- and $4$-manifold topology, used to construct manifolds and to prove that two of them are diffeomorphic.\n\n## Explanations\n\n### L1 human\n\nEvery closed orientable $3$-dimensional space can be drawn as a picture of knotted loops in ordinary space, each labelled by an integer.\nMany different pictures describe the same space.\nKirby calculus is the list of allowed picture changes, a little like the rules for simplifying an algebraic expression.\nFor example, a single unknotted loop labelled $+1$ or $-1$, far away from the other loops, can be added or erased.\nThis does not change the space, and the loop alone describes the $3$-sphere.\n",
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