Trisections of PL 4-manifolds arising from colored triangulations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910801928912896 |
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| author | Casali, Maria Rita Cristofori, Paola |
| author_facet | Casali, Maria Rita Cristofori, Paola |
| contents | The purpose of the present paper is twofold: firstly to extend to non-orientable compact 4-manifolds the notion of gem-induced trisection, directly obtained from colored triangulations (or, equivalently, from colored graphs encoding them, called gems); secondly to prove that, both in the orientable and non-orientable case, if the boundary is homeomorphic to a connected sum of sphere bundles over $\mathbb S^1$, gem-induced trisections naturally give rise to trisections of the corresponding closed 4-manifold. As a consequence, an estimation of the trisection genus of any closed orientable 4-manifold in terms of surgery description is obtained via colored triangulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01902 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Trisections of PL 4-manifolds arising from colored triangulations Casali, Maria Rita Cristofori, Paola Geometric Topology 57Q15 - 57K40 - 57M15 The purpose of the present paper is twofold: firstly to extend to non-orientable compact 4-manifolds the notion of gem-induced trisection, directly obtained from colored triangulations (or, equivalently, from colored graphs encoding them, called gems); secondly to prove that, both in the orientable and non-orientable case, if the boundary is homeomorphic to a connected sum of sphere bundles over $\mathbb S^1$, gem-induced trisections naturally give rise to trisections of the corresponding closed 4-manifold. As a consequence, an estimation of the trisection genus of any closed orientable 4-manifold in terms of surgery description is obtained via colored triangulations. |
| title | Trisections of PL 4-manifolds arising from colored triangulations |
| topic | Geometric Topology 57Q15 - 57K40 - 57M15 |
| url | https://arxiv.org/abs/2312.01902 |