bracket polynomial

《Symplectic Geometry》 · 第 217–219 页 · Section 9.2，Definition 9.2.1 的三个公理及 Figure 9.1 原图

The bracket polynomial of an unoriented diagram \(D\), denoted by \(\langle D\rangle\), is a Laurent polynomial in a single variable \(A\) defined by the three following axioms. 1. Normalisation: \(\langle O\rangle=1\) where \(O\) denotes the diagram of one component and no crossings. 2. Delta: \(\langle D\cup O\rangle=\delta\langle D\rangle\) where \(\delta=-A^{-2}-A^2\) and \(D\cup O\) denotes the diagram \(D\) together with a single component that does not cross itself or \(D\). 3. Skein relation: \(\langle D_+\rangle=A\langle D_0\rangle+A^{-1}\langle D_\infty\rangle\) where diagrams \(D_+,D_0,D_\infty\) differ as shown in Figure 9.1.