Knots and Their Polynomials-11

 Knots and Their Polynomials


Food for thought

Figure-Eight

  • 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.