TQFT / Chern-Simons & Jones Polynomial
Kauffman Bracket · Skein Relations · q-Deformation
Knot Selection
Unknot
Trefoil
Figure-8
Hopf Link
q param
i
Anim Speed
5
Compute Jones
Animate Skein
Skein Relations (Kauffman Bracket)
⟨ ⟩ = A·⟨ )( ⟩ + A⁻¹·⟨ ∞ ⟩
⟨L ⊔ ○⟩ = δ·⟨L⟩, δ = −A² − A⁻²
⟨○⟩ = 1
Jones: V_L(t) = (−A³)^(−w) · ⟨L⟩
where A = t^(−1/4), w = writhe
Computation Steps
Select a knot and click
Compute Jones
to see step-by-step Kauffman bracket evaluation.
Jones Polynomial Result
Awaiting computation...
q-Deformation: Quantum Trace