Knots and Their Polynomials

Food for thought

• Calculate the Jones polynomial of the figure-eight knot.

• What happens to the polynomial when you change the crossings?

• How should this be interpreted?

Square knot.

• Show that when two knots are spliced together, the Jones polynomialof the splice is the product of the two Jones polynomials.

• Calculate the Jones polynomial of (left-trefoil) splice (right-trefoil)= square knot.

• Calculate the Jones polynomials of (left-trefoil) splice (left-trefoil)and (right-trefoil) splice (right-trefoil) = two granny knots.

Back to the previous knot page.

Back to the first knot page.