Chern-Simons theory is a 3D topological quantum field theory whose partition function
and Wilson loop expectation values compute topological link invariants. For gauge group SU(2) at level k,
the path integral Z = ∫DA e^{iS_CS[A]} with Wilson loops W_R[C] = Tr_R P exp(i∮_C A)
computes the Jones polynomial (Witten 1989, Fields Medal):
⟨W_R[L]⟩ = V_L(q) with q = e^{2πi/(k+2)}.
The skein relation Δ⁺V₊ − Δ⁻V₋ = (√q − 1/√q)V₀ determines the polynomial recursively.
The visualization shows 3D projections of standard links as animated space curves, with their crossing data,
writhe (w), and computed link invariants.