Quantum invariant of 3-manifolds

Summary

Quantum invariants of $3$-manifolds are invariants of closed oriented 3-manifolds. They are built from the representation theory of quantum groups at roots of unity, or more generally from modular tensor categories. The main examples are the Witten–Reshetikhin–Turaev invariants, which Witten predicted from quantum Chern–Simons theory and Reshetikhin and Turaev constructed rigorously. They are computed from a surgery presentation of the manifold, using colored versions of the Jones polynomial. They are part of topological quantum field theories in dimension $3$.