closed braid

《Symplectic Geometry》 · 第 241 页 · Section 10.1，Definition 10.1.1 及 open-book 半平面坐标

Think of \(\mathbb R^3\) as \(\mathbb C\times\mathbb R\) with coordinate system \((r,\theta,z)\). The \(z\)-axis will be the binding for the book. […] For a fixed value of \(\theta\) the set \(H_\theta=\{(r,\theta,z)\in\mathbb R^3\}\) is the half-plane at angle \(\theta\). […] A link \(L\subset\mathbb R^3\) is presented as a closed \(n\)-string braid if \(L\) meets every page \(H_\theta\) transversely in \(n\) points. The binding of the open-book decomposition is called the braid axis. If the link is oriented then all the components must travel around the axis in the same direction.