Properties of minimal charts and their applications IX: charts of type (4,3)
Properties of minimal charts and their applications IX: charts of type (4,3)
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最小图表的性质及其应用九：(4,3)类型的图表
DOI：
10.1016/j.indag.2023.01.009
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Shima Akiko
中科院分区：
文献类型：
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作者：
Nagase Teruo;Shima Akiko
图表是磁盘中有方向标记的图形。任何简单的表面编织（二维编织）都可以用图表来描述。此外，图表表示嵌入在四维空间中的定向闭合曲面。本文利用图的方法研究四维空间中的嵌入曲面。设Γ是一个图，我们用Γ m表示标号m的所有边的并集。图Γ是（4，3）型图，如果存在标号m使得w（Γ）= 7，w（Γ m <$Γ m+ 1）= 4，w（Γ m+ 1 <$Γ m+ 2）= 3其中w（G）是G中白色点的个数.本文证明了不存在（4，3）型极小图。
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 (4, 3) if there exists a label m such that w (Γ)= 7, w (Γ m∩ Γ m+ 1)= 4, w (Γ m+ 1∩ Γ m+ 2)= 3 where w (G) is the number of white vertices in G. In this paper, we prove that there is no minimal chart of type (4, 3).