Mathematical Physics: Classical Mechanics
《Mathematical Physics: Classical Mechanics》 · 第 190 页 · Chapter 16 末段，Vassiliev invariants 的定义与 Figure 16.3（正文误称 Figure 16.2）
Suppose \(V\) is any invariant of oriented links taking values in some abelian group. This \(V\) be can extended to be an invariant of singular links in the following way: A singular link is an immersion of simple closed curves in \(S^3\) with finitely many transverse double points. These self-intersections are required to remain transverse in any isotopy demonstrating the equivalence of such singular links. If the definition of \(V\) has been extended over singular links with \(n-1\) double points, define it on a singular link \(L_\times\) with \(n\) singularities by \(V(L_\times)=V(L_+)-V(L_-)\), where \(V(L_\times),V(L_+),V(L_-)\) are identical except near a point where they are as in Figure 16.2. Note that \(V(L_+)\) and \(V(L_-)\) each has \(n-1\) double points. Then \(V\) is called a Vassiliev invariant of order \(n\), or an invariant of finite type \(n\), if \(V(L)=0\) for every \(L\) with \(n+1\) or more singularities.