Knots and their polynomials

The Calculation of the Jones Polynomial of the Right Trefoil

• Step 1: from the Right Trefoil to the Right Link

• Step 2: from the Right Link to two unlinked unknots

• Step 3: the Jones Polynomial of two unlinked unknots

• Step 4: Working backwards to the answer

• [t] = - t^1/2 - t^-1/2. (Step 3)

• [t] = t^3/2 - t^1/2 + t² [t] (Step 2)
  = t^3/2 - t^1/2 + t² (- t^1/2 - t^-1/2)

  = -t^5/2 - t^1/2.

• [t] = (t^3/2 - t^1/2) [t] + t² (Step 1)
  = (t^3/2 - t^1/2) (- t^5/2 - t^1/2) + t²

  = -t⁴ + t³ + t.

Back to the previous step.

Back to the first knot page.