Heegaard diagrams for $5$-manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910937722650624 |
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| author | Kim, Geunyoung |
| author_facet | Kim, Geunyoung |
| contents | We introduce a version of Heegaard diagrams for $5$-dimensional cobordisms with $2$- and $3$-handles, $5$-dimensional $3$-handlebodies, and closed $5$-manifolds. We show that every such smooth $5$-manifold can be represented by a Heegaard diagram, and that two Heegaard diagrams represent diffeomorphic $5$-manifolds if and only if they are related by certain moves. As an application, we construct Heegaard diagrams for $5$-dimensional cobordisms from the standard $4$-sphere to the Gluck twists along knotted $2$-spheres. This provides several statements equivalent to the Gluck twist being diffeomorphic to the standard $4$-sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06887 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heegaard diagrams for $5$-manifolds Kim, Geunyoung Geometric Topology 57K40, 57K50, 57R65 We introduce a version of Heegaard diagrams for $5$-dimensional cobordisms with $2$- and $3$-handles, $5$-dimensional $3$-handlebodies, and closed $5$-manifolds. We show that every such smooth $5$-manifold can be represented by a Heegaard diagram, and that two Heegaard diagrams represent diffeomorphic $5$-manifolds if and only if they are related by certain moves. As an application, we construct Heegaard diagrams for $5$-dimensional cobordisms from the standard $4$-sphere to the Gluck twists along knotted $2$-spheres. This provides several statements equivalent to the Gluck twist being diffeomorphic to the standard $4$-sphere. |
| title | Heegaard diagrams for $5$-manifolds |
| topic | Geometric Topology 57K40, 57K50, 57R65 |
| url | https://arxiv.org/abs/2505.06887 |