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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/2509.14299 |
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| _version_ | 1866918143292604416 |
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| author | Lawande, Shital Saha, Kuldeep |
| author_facet | Lawande, Shital Saha, Kuldeep |
| contents | Following a recent work of Kastenholz, we show existence of infinitely many parallelizable closed oriented 4-manifolds, none of which admit an open book decomposition. This implies there is no analogue of the Giroux correspondence for Engel manifolds. In particular, not every Engel manifold has a supporting open book, in the sense of Colin, Presas and Vogel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14299 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 4-manifolds and non-existence of open book Lawande, Shital Saha, Kuldeep Geometric Topology Following a recent work of Kastenholz, we show existence of infinitely many parallelizable closed oriented 4-manifolds, none of which admit an open book decomposition. This implies there is no analogue of the Giroux correspondence for Engel manifolds. In particular, not every Engel manifold has a supporting open book, in the sense of Colin, Presas and Vogel. |
| title | 4-manifolds and non-existence of open book |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2509.14299 |