Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper...Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;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.展开更多
基金The NSF(11601209)of ChinaResearch Foundation(201601239)for Doctor of Liaoning Province+1 种基金Scientific Research Fund(L201683660)of Liaoning Provincial Education DepartmentYouth Foundation(LS2015L002)of Liaoning Normal University
文摘Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;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.
