A one-variable Knot Polynomial related to the Jones Polynomial. The bracket polynomial, however, is *not* a
topological invariant, since it is changed by type I Reidemeister Moves. However, the Span
of the bracket polynomial is a knot invariant. The bracket polynomial is occasionally given the grandiose name Regular
Isotopy Invariant. It is defined by

(1) |

(2) |

(3) | |||

(4) |

gives a Knot Polynomial which is invariant under Regular Isotopy, and normalizing gives the Kauffman Polynomial

(5) | |||

(6) | |||

(7) |

where is the Writhe of .

**References**

Adams, C. C. *The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.* New York:
W. H. Freeman, pp. 148-155, 1994.

Kauffman, L. ``New Invariants in the Theory of Knots.'' *Amer. Math. Monthly* **95**, 195-242, 1988.

Kauffman, L. *Knots and Physics.* Teaneck, NJ: World Scientific, pp. 26-29, 1991.

Weisstein, E. W. ``Knots and Links.'' Mathematica notebook Knots.m.

© 1996-9

1999-05-26