Embeddings of 3-manifolds via open books

We prove that every open book decomposition of a closed orientable 3-manifold admits open book embedding in every open book decomposition of S2×S3 and S2sim;×S3 with page a disk bundle over S2 and monodromy the identity map. As an application of our methods, we give a new proof of a classical result of Hirsch which says that every closed orientable 3-manifold embeds in S5.