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 - <p style="text-align: justify;">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&nbsp;$\partial_-V$ 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.</p>