BracketInvariant

The writhe-corrected Kauffman bracket $(-A^3)^{-w}\langle L\rangle$ of a knot or link — already an invariant, unlike KauffmanBracket on its own.

BracketInvariant(knot)$(-A^3)^{-w}\langle L\rangle$, already an invariant

Typed signatures

Type	Package	Applies
(expression<Braid> | expression<FigureEightKnot> | expression<Link> | expression<PretzelKnot> | expression<TorusKnot> | expression<TwistKnot> | string) -> expression	braid	always

Domain: Braids and knots

Examples

Basic #

The writhe-corrected bracket of $T(2,3)$

live ↗

In$\mathrm{BracketInvariant}(\mathrm{TorusKnot}(2, 3))$Out$-\frac{1}{A^{16}}+\frac{1}{A^{12}}+\frac{1}{A^4}$

Amphichiral: symmetric under $A\mapsto A^{-1}$

live ↗

In$\mathrm{BracketInvariant}(\mathrm{FigureEightKnot}())$Out$A^8-A^4-\frac{1}{A^4}+\frac{1}{A^8}+1$

About

Examples	2

See also: KauffmanBracket, JonesPolynomial, BraidWrithe