What is "open book decomposition"

n. (context mathematics topology English) A decomposition of a 3-manifold into a link and a fibration over the circle by surfaces bounded by that link.

In mathematics, an open book decomposition (or simply an open book) is a decomposition of a closed oriented 3-manifold M into a union of surfaces (necessarily with boundary) and solid tori. Open books have relevance to contact geometry, with a famous theorem of Emmanuel Giroux (given below) that shows that contact geometry can be studied from an entirely topological viewpoint.