Weakly Disk-busting Curves in the Boundary of a Compression Body

摘要

Let V be a nontrivial compression body which is not simple.An essential simple closed curve J in (З)+ V is called weakly disk-busting if (З)+ V-J has only one compressing disk up to isotopy.In this paper,we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve.Moreover,we give a sufficient condition for the handle additions to be boundary irreducible.