Chern-Simons Theory — Link Invariants & Hopf Fibration

Chern-Simons theory assigns topological invariants to knots and links via Wilson loop expectation values. The Jones polynomial emerges as the partition function on S³. Here we visualise (p,q)-torus knots/links — curves wrapping p times around the torus meridian and q times around its longitude — and compute their linking number and writhe, the classical precursors to quantum invariants.

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Knot/Link type
Linking number Lk
Writhe (classical)