# Tag Info

Quantum topology begins with the discovery of the Jones polynomial of an oriented knot or link, and its relationships with statistical mechanics and with quantum groups. Edward Witten showed how the Jones polynomial may be recovered physically from Chern-Simons theory on the 3-sphere with gauge group $SU(2)$. By way of singularity theory, Victor Vassiliev discovered the finite-type invariants, placing the Jones polynomial in a broader framework. These are organized by the universal finite-type invariant, that is the Kontsevich invariant. Meanwhile, quantum topological invariants of 3-manifolds such as the Turaev-Viro invariants and the Reshetikhin-Turaev invariants were also discovered.