Properties of minimal charts and their applications X: charts of type $(5,2)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913397290827776 |
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| author | Nagase, Teruo Shima, Akiko |
| author_facet | Nagase, Teruo Shima, Akiko |
| contents | Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface embedded in 4-space. In this paper, we investigate embedded surfaces in 4-space by using charts. Let $Γ$ be a chart, and we denote by $Γ_m$ the union of all the edges of label $m$. A chart $Γ$ is of type $(5,2)$ if there exists a label $m$ such that $w(Γ)=7$, $w(Γ_m\capΓ_{m+1})=5$, $w(Γ_{m+1}\capΓ_{m+2})=2$ where $w(G)$ is the number of white vertices in $G$. In this paper, we investigate a minimal chart of type $(5,2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12865 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties of minimal charts and their applications X: charts of type $(5,2)$ Nagase, Teruo Shima, Akiko Geometric Topology 57K45, 05C10, 57M15 Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensional braid) can be described by using a chart. Also, a chart represents an oriented closed surface embedded in 4-space. In this paper, we investigate embedded surfaces in 4-space by using charts. Let $Γ$ be a chart, and we denote by $Γ_m$ the union of all the edges of label $m$. A chart $Γ$ is of type $(5,2)$ if there exists a label $m$ such that $w(Γ)=7$, $w(Γ_m\capΓ_{m+1})=5$, $w(Γ_{m+1}\capΓ_{m+2})=2$ where $w(G)$ is the number of white vertices in $G$. In this paper, we investigate a minimal chart of type $(5,2)$. |
| title | Properties of minimal charts and their applications X: charts of type $(5,2)$ |
| topic | Geometric Topology 57K45, 05C10, 57M15 |
| url | https://arxiv.org/abs/2406.12865 |