TY - JOUR T1 - Weakly Disk-Busting Curves in the Boundary of a Compression Body AU - Sun , Meng AU - Liang , Liang JO - Communications in Mathematical Research VL - 2 SP - 171 EP - 176 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.02.09 UR - https://global-sci.org/intro/article_detail/cmr/13524.html KW - handle addition, curve complex, subsurface projection, weakly disk-busting AB -

Let $V$ be a nontrivial compression body which is not simple. An essential simple closed curve $J$ in $\partial_+V$ is called weakly disk-busting if $\partial_+V-J$ 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.