Properties of minimal charts and their applications X: charts of type (5,2)

2024/03/22 by Nagase, Teruo, Shima, Akiko
#05C10 #57K45 #57M15 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2406.12865

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 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∩Γ_m+1)=5, w(Γ_m+1∩Γ_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).

Related

• Properties of minimal charts and their applications IX: charts of type (4,3)
• Properties of minimal charts and their applications XI: no minimal charts with exactly seven white vertices
• The linear minimal 4-chart with three crossings
• Properties of minimal charts and their applications V: charts of type (3,2,2)
• Properties of minimal charts and their applications VII: charts of type (2,3,2)