Weakly Disk-Busting Curves in the Boundary of a Compression Body (Communications in Mathematical Research, 2019)
Let $V$ be a nontrivial compression body which is not simple. An essentialsimple closed curve $J$ in $\partial_+V$ is called weakly disk-busting if $\partial_+V-J$ has only onecompressing disk up to isotopy. In this paper, we give an upper bound of the diameterof the image of boundaries of essential disks in $V$ under any projection determined bya weakly disk-busting curve. Moreover, we give a sufficient condition for the handleadditions to be boundary irreducible.
Keywords: handle addition; curve complex; subsurface projection; weakly disk-busting