Properties of Minimal Charts and Their Applications X: Charts of Type (5, 2)
Vol. 33 (2026), No. 1, Page 49-96.
Nagase, T.; Shima, A.
Properties of Minimal Charts and Their Applications X: Charts of Type (5, 2)
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Abstract:
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 $\Gamma$ be a chart, and we denote by $\Gamma_m$ the union of all the edges of label $m$. A chart $\Gamma$ is of type $(5,2)$ if there exists a label $m$ such that $w(\Gamma)=7$, $w(\Gamma_m\cap\Gamma_{m+1})=5$, $w(\Gamma_{m+1}\cap\Gamma_{m+2})=2$ where $w(G)$ is the number of white vertices in $G$. In this paper, we investigate a minimal chart of type (5,2).
Keywords: surface-link, chart, C-move, white vertex
Mathematics Subject Classification (2020): Primary 57K45, 05C10; Secondary 57M15.
Received: 2024-07-22
