Talk:Open book decomposition

I thought that Lawsons theorem is just about odd-dimensional spheres, not about arbitrary odd-dimensional manifolds? --Suhagja (talk) 07:38, 23 January 2013 (UTC)

Why call it a "fibration" if it is fact a fibre bundle?

The section Definition and construction begins as follows:

"Definition. An open book decomposition of a 3-dimensional manifold M is a pair (B, π) where

• B is an oriented link in M, called the binding of the open book;
• π: M \ B → S¹ is a fibration of the complement of B such that for each θ ∈ S¹, π⁻¹(θ) is the interior of a compact surface Σ ⊂ M whose boundary is B. The surface Σ is called the page of the open book."

A "fibration" is a generalization of a fibre bundle.

But isn't π : M \ B → S¹ a genuine fibre bundle projection?

If this is correct, it is much better to label π as such, rather than the much more general concept of a fibration.

I hope someone familiar with this subject can make this definition more precise.