Multisections of higher-dimensional manifolds
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916511329812480 |
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| author | Aribi, Fathi Ben Courte, Sylvain Golla, Marco Moussard, Delphine |
| author_facet | Aribi, Fathi Ben Courte, Sylvain Golla, Marco Moussard, Delphine |
| contents | Generalizing Heegaard splittings of 3-manifolds and trisections of 4-manifolds, we consider multisections of higher-dimensional smooth (or PL) closed orientable manifolds, namely decompositions into 1-handlebodies whose subcollections intersect along 1-handlebodies, with global intersection a closed surface. With such a multisection one can associate a diagram. We prove that a multisection diagram determines a unique PL-manifold in all dimensions and a unique smooth manifold up to dimension 6. Further, we show that any closed orientable smooth 5-manifold admits a multisection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_08779 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Multisections of higher-dimensional manifolds Aribi, Fathi Ben Courte, Sylvain Golla, Marco Moussard, Delphine Geometric Topology 57K50, 57M99 Generalizing Heegaard splittings of 3-manifolds and trisections of 4-manifolds, we consider multisections of higher-dimensional smooth (or PL) closed orientable manifolds, namely decompositions into 1-handlebodies whose subcollections intersect along 1-handlebodies, with global intersection a closed surface. With such a multisection one can associate a diagram. We prove that a multisection diagram determines a unique PL-manifold in all dimensions and a unique smooth manifold up to dimension 6. Further, we show that any closed orientable smooth 5-manifold admits a multisection. |
| title | Multisections of higher-dimensional manifolds |
| topic | Geometric Topology 57K50, 57M99 |
| url | https://arxiv.org/abs/2303.08779 |