TY - JOUR T1 - Spanning Pre-Disks in a Compression Body AU - Liang , Liang AU - Han , Youfa AU - Li , Fengling AU - Zhao , Luying JO - Communications in Mathematical Research VL - 2 SP - 177 EP - 183 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.02.10 UR - https://global-sci.org/intro/article_detail/cmr/13522.html KW - spanning pre-disk, curve complex, compression body, maximal collection AB -

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 $\partial_+V$ 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 number of a maximal collection of spanning pre-disks is bounded.