The goal of this paper is to find the Homfly polynomial for each knot in a specific family of knots. This family of knots is generated from placing the Whitehead link into a solid torus, slicing the torus at a spot where the Whitehead has no crossings and then twisting the torus 360 degrees in either direction an integral number of times. Let L(n) denote the knot obtained by twisting the torus 360 degrees, n times. Note that n is an integer. Let the twists be towards the center of the torus for positive n and away from the center for negative n. Through the obtained Homfly polynomials, it will be determined that each of the knots in this family are distinct and non-trivial (excepting the Whitehead link).
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Roberts, Sharleen Adrienne, "Knots Not for Naught" (2006). Theses and Dissertations. 735.
whitehead, link, knot, homfly