A note on codimension $2$ spun embedding

Sneha Banerjee; Shital Lawande; Subhadeep Rana; Kuldeep Saha

A note on codimension $2$ spun embedding

Geometric Topology 2025-11-07 v1

Authors: Sneha Banerjee , Shital Lawande , Subhadeep Rana , Kuldeep Saha

Abstract

We prove that if a closed manifold $B$ is a connected component of the binding of an open book decomposition of a manifold $M$ , then every open book decomposition of $B$ spun embeds in $M$ . As an application, we prove that every open book decomposition of a simply connected spin $5$ -manifold spun embeds in $S^7$ and every $3$ -dimensional open book spun embeds in $S^5$ . We also define a notion of spun embedding for Morse open books.

Cite

@article{arxiv.2511.03812,
  title  = {A note on codimension $2$ spun embedding},
  author = {Sneha Banerjee and Shital Lawande and Subhadeep Rana and Kuldeep Saha},
  journal= {arXiv preprint arXiv:2511.03812},
  year   = {2025}
}

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