Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 17 (2010), No. 2, Page 217-241
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 Γ with at most two crossings is a ribbon chart provided that the closure of the surface braid represented by Γ is a disjoint union of spheres.