Abstract :

We discuss embeddings of 3–manifolds via open books. First we show that every open book of every closed orientable 3–manifold admits an open book embedding in any open book decompistion of $S^2 X S^3$ and twisted $S^2X S^3$ with the page a disk bundle over $S^2$ and monodromy the identity. We then use open book embeddings to reprove Hrirsch's that every closed orientable 3–manifold embeds in $S^5$.