Properties of Minimal Charts and Their Applications IV: Loops

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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
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Abstract:
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.

Keywords: 2-knot, chart, white vertex.

Mathematics Subject Classification (2010): Primary 57Q45; Secondary 57Q35.

Mathematical Reviews Number: MR3674447

Received: 2016-03-16

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