Spanning Pre-disks in a Compression Body

摘要

A properly embedded essential planar surface P(not a disk) in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?_+V and all other boundary components of P are lying in?_-V and coplanar with J. In this paper, we show that the number of boundary components of spanning pre-disks in a compression body is unbounded. But the number of a maximal collection of spanning pre-disks is bounded.