Commun. Math. Res., 34 (2018), pp. 171-176.
Published online: 2019-12
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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} }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.