Spanning Pre-Disks in a Compression Body (Communications in Mathematical Research, 2019)
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 boundarycomponent of $P$ is lying in $\partial_+V$ and all other boundary components of $P$ are lying in $\partial_-V$ 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 numberof a maximal collection of spanning pre-disks is bounded.