Abstract
In this note, we discuss open book embeddings of closed non-orientable $3$-manifolds in $5$-manifolds. We also show that a huge class of closed orientable $3$-manifolds, namely the orientation double covers of certain closed non-orientable $3$-manifolds, open book embeds in the $5$-sphere $S^5$. Finally, we give a new proof of a well-known theorem which states that every closed non-orientable $3$-manifold smoothly embeds in $S^5$.
Citation
Abhijeet Ghanwat. Suhas Pandit. Selvakumar A. "Open book embeddings of closed non-orientable $3$-manifolds." Rocky Mountain J. Math. 49 (4) 1143 - 1168, 2019. https://doi.org/10.1216/RMJ-2019-49-4-1143