Properties of minimal charts and their applications VI: the graph Γ_m+1 in a chart Γ of type (m;2,3,2)

2020/03/25 by Nagase, Teruo, Shima, Akiko
#57Q35 #57Q45 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2003.11909

Abstract

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 (m;2,3,2) if w(Γ)=7, w(Γ_m∩Γ_m+1)=2, w(Γ_m+1∩Γ_m+2)=3, and w(Γ_m+2∩Γ_m+3)=2 where w(G) is the number of white vertices in G. In this paper, we prove that if there is a minimal chart Γ of type (m;2,3,2), then each of Γ_m+1 and Γ_m+2 contains one of three kinds of graphs. In the next paper, we shall prove that there is no minimal chart of type (m;2,3,2).

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