Properties of minimal charts and their applications V: charts of type (3,2,2)

2019/01/31 by Nagase, Teruo, Shima, Akiko
#FOS: Mathematics #Geometric Topology (math.GT) #Primary 57Q45 #Secondary 57Q35

paper · doi:10.48550/arxiv.1902.00007

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 (3,2,2) if there exists a label m such that w(Γ)=7, w(Γ_m∩Γ_m+1)=3, w(Γ_m+1∩Γ_m+2)=2, 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 there is no minimal chart of type (3,2,2).

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