High Quality Content by WIKIPEDIA articles! 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.When is an oriented compact surface with n boundary components and : -> is a homeomorphism which is the identity near the boundary, we can construct an open book by first forming the mapping torus . Since is the identity on , is the trivial circle bundle over a union of circles, that is, a union of tori. To complete the construction, solid tori are glued to fill in the boundary tori so that each circle S1 x {p} S1x D2 is identified with the boundary of a page. In this case, the binding is the collection of n cores S1x{q} of the n solid tori glued into the mapping torus, for arbitrarily chosen q D2. It is known that any open book can be constructed this way.

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