@Article{CMR-34-171, author = {Sun , Meng and Liang , Liang}, title = {Weakly Disk-Busting Curves in the Boundary of a Compression Body}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {2}, pages = {171--176}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.02.09}, url = {http://global-sci.org/intro/article_detail/cmr/13524.html} }