Chern-Simons TQFT — Knot Invariants & Jones Polynomials

Knot type: Unknot Trefoil (3₁) Hopf Link (2²₁) Figure-Eight (4₁) Cinquefoil (5₁) Level k: 5 Animate skein:

Chern-Simons theory with gauge group SU(2) at level k assigns a quantum invariant to each knot. The Jones polynomial V(q) evaluated at q=exp(2πi/(k+2)) equals the Chern-Simons partition function — computed here via skein relations: V(L₊) − V(L₋) = (q^½ − q^-½)V(L₀).