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Knots and Their Polynomials-6

 Knots and Their Polynomials

The calculation of the Jones polynomial of the right trefoil

The next step is to analyze that link by the same method.

t-1J(right-link)[t] - t J(two unlinked unknots)[t] =(t1/2 - t-1/2) J(right-link-switched)[t].

This time the knot on the right is topologically an unknot:

right-link-switched =unknot,so J(right-link-switched)[t] = 1,

which gives

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

On to the next step.

Back to the previous step.

Back to the first knot page.