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  "body": "\n## Summary\n\nQuantum invariants of $3$-manifolds are invariants of closed oriented [[3-manifolds|R20TB2KEQQ]].\nThey are built from the representation theory of [[quantum groups|AP2ZDXANKC]] at roots of unity, or more generally from modular tensor categories.\nThe main examples are the Witten–Reshetikhin–Turaev invariants, which Witten predicted from quantum [[Chern–Simons theory|F28G886PWD]] and Reshetikhin and Turaev constructed rigorously.\nThey are computed from a surgery presentation of the manifold, using colored versions of the [[Jones polynomial|4SPC17FPXE]].\nThey are part of [[topological quantum field theories|DAP92B80J2]] in dimension $3$.\n\n## Explanations\n\n### L1 human\n\nEvery closed oriented $3$-manifold can be obtained by surgery on a link in the $3$-sphere, but in many different ways.\nA quantum invariant assigns a number to the link, built from knot polynomials, and corrects it so that the number does not depend on which link is chosen.\nThe result is a number attached to the manifold itself.\nThese numbers can be computed from a picture of the link, yet their geometric meaning is still only partly understood.\n",
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