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) |
(5) | |||
(6) | |||
(7) |
See also Square Bracket Polynomial
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 Eric W. Weisstein