Embeddings of 3--manifolds via open books

Abstract

In this note, 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 S2×S3 and S2טS3 with the page a disk bundle over S2 and monodromy the identity. We then use open book embeddings to reprove that every closed orientable 3--manifold embeds in S5.