Embeddings of $3$--manifolds via open books

Dishant M. Pancholi; Suhas Pandit; Kuldeep Saha

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arXiv · 1806.09784

Embeddings of $3$--manifolds via open books

Dishant M. Pancholi·Suhas Pandit·Kuldeep Saha

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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 $S^2 \times S^3$ and $S^2 \widetilde{\times} S^3$ with the page a disk bundle over $S^2$ and monodromy the identity. We then use open book embeddings to reprove that every closed orientable $3$--manifold embeds in $S^5.$

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Dishant M. Pancholi, Suhas Pandit, Kuldeep Saha. 2018-06-26. Embeddings of $3$--manifolds via open books. https://arxiv.org/abs/1806.09784

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