On Charts with Two Crossings I: There Exist No NS-Tangles in a Minimal Chart

J. Math. Sci. Univ. Tokyo
Vol. 17 (2010), No. 2, Page 217--241.

Nagase, Teruo; Shima, Akiko
On Charts with Two Crossings I: There Exist No NS-Tangles in a Minimal Chart
In this paper, we establish methods to count the number of crossings and terminal edges of charts. These methods are useful to show that a chart $\Gamma$ with at most two crossings is a ribbon chart provided that the closure of the surface braid represented by $\Gamma$ is a disjoint union of spheres.