Knots and Their Polynomials-8

 Knots and Their Polynomials


The calculation of the Jones polynomial of the right trefoil

  • J(two unlinked unknots)[t]=- t1/2 - t-1/2. (Step 3)

  • J(right-link)[t] =t3/2 - t1/2 + t2 J(two unlinked unknots)[t] (Step 2)

    = t3/2 - t1/2 + t2 (- t1/2 - t-1/2)

    = -t5/2 - t1/2.

  • J(right-trefoil)[t] =(t3/2 - t1/2)J(right-link)[t] + t2 (Step 1)

    = (t3/2 - t1/2)(- t5/2 - t1/2) +t2

    = -t4 + t3 + t.

This completes the calculation.


On to the next knot page.

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