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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2509.06168 |
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| _version_ | 1866914027098079232 |
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| author | Lawande, Shital Saha, Kuldeep |
| author_facet | Lawande, Shital Saha, Kuldeep |
| contents | We study codimension $1$ embeddings preserving open book structures. In particular, we prove that every closed orientable 3-manifold admits a codimension-1 spun embedding in a finite connected sum of $S^2 \times S^2$s and $S^2 \tilde{\times} S^2$s. We discuss some explicit constructions of planar open books on 3-manifolds and their codimension $1$ spun embeddings. To construct these embeddings, we use sphere twist maps and push maps. We also give a simple proof for nontriviality of the twist map along a nonseparating $S^n$ in the group of orientation preserving diffeomorphisms of $S^1 \times S^n \setminus D^{n+1}$, relative to the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Twist maps and codimension-1 spun embeddings Lawande, Shital Saha, Kuldeep Geometric Topology We study codimension $1$ embeddings preserving open book structures. In particular, we prove that every closed orientable 3-manifold admits a codimension-1 spun embedding in a finite connected sum of $S^2 \times S^2$s and $S^2 \tilde{\times} S^2$s. We discuss some explicit constructions of planar open books on 3-manifolds and their codimension $1$ spun embeddings. To construct these embeddings, we use sphere twist maps and push maps. We also give a simple proof for nontriviality of the twist map along a nonseparating $S^n$ in the group of orientation preserving diffeomorphisms of $S^1 \times S^n \setminus D^{n+1}$, relative to the boundary. |
| title | Twist maps and codimension-1 spun embeddings |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2509.06168 |