Co-dimension two spinal open book embeddings of 3-manifolds

In this paper, we show that every spinal open book decomposition of a closed oriented 3-manifold M spinal open book embeds into a certain spinal open book decomposition of #kS2×S3, the connected sum of k copies of the twisted S3-bundle over S2, where k depends on the spinal open book decomposition of M. We also discuss spinal open book embeddings of a huge class of spinal open books of closed oriented 3-manifolds into the trivial spinal open book of the 5-sphere S5. Finally, we show that given a closed oriented 3-manifold M, there exists a spinal open book for M such that M spinal open book embeds into the trivial spinal open book of S5. In particular, this gives another proof of Hirsch's theorem which states that every closed orientable 3-manifold embeds in S5.