Properties of minimal charts and their applications IX: charts of type (4,3)

2022/07/24 by Nagase, Teruo, Shima, Akiko
#05C10 #57K45 #57M15 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2207.11715

Abstract

Charts are oriented labeled graphs in a disk. Any simple surface braid (2-dimensonal 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).

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