## Properties of Minimal Charts and Their Applications IV: Loops

J. Math. Sci. Univ. Tokyo
Vol. 24 (2017), No. 2, Page 195–237.

Nagase, Teruo ; Shima, Akiko
Properties of Minimal Charts and Their Applications IV: Loops
We investigate minimal charts with loops, a simple closed curve consisting of edges of label $m$ containing exactly one white vertex. We shall show that there does not exist any loop in a minimal chart with exactly seven white vertices in this paper.