Symplectic Geometry
《Symplectic Geometry》 · 第 139 页 · Section 6.5，Seifert pairing 的定义（连通有向曲面）
In this section we shall explore a technique for studying the embeddings of connected oriented surfaces in \(\mathbb R^3\). […] Let \(b:F\times[-1,1]\longrightarrow\mathbb R^3\) be a homeomorphism such that \(b(F\times\{0\})=F\) and \(b(F\times\{1\})\) lies on the positive side of \(F\). Any subset \(X\subset F\) can be lifted out of the surface on either side: we let \(X^+=b(X\times\{1\})\) and \(X^-=b(X\times\{-1\})\). […] We can use this to define the following mapping: \(\Theta:H_1(F)\times H_1(F)\longrightarrow\mathbb Z\), \((a,b)\longmapsto\operatorname{lk}(a,b^+)\). This is called the Seifert pairing or linking form of the embedded surface.