Abstract
Let $\Gamma$ be a chart with at most two crossings. In this paper, we show that if $\Gamma$ is a 2-minimal generalized $n$-chart with $n \ge 5$, then $\Gamma$ contains at least $4n-10$ black vertices. And we show that if the closure of the surface braid represented by $\Gamma$ is a disjoint union of spheres, then $\Gamma$ is a ribbon chart. Hence the closure is a ribbon surface.
Citation
Teruo Nagase. Akiko Shima. "On charts with two crossings II." Osaka J. Math. 49 (4) 909 - 929, December 2012.
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