A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of...A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of P are lying in?;V and coplanar with J. In this paper, we show that the number of boundary components of spanning pre-disks in a compression body is unbounded. But the number of a maximal collection of spanning pre-disks is bounded.展开更多
基金The NSF(11601209,11471151,11401069 and 11671064)of Chinathe Research Foundation (201601239)for Doctor of Liaoning Province+2 种基金the Scientific Research Fund(L201683660)of Liaoning Provincial Education Departmentthe Youth Foundation(LS2015L002)of Liaoning Normal Universitya grant of the Fundamental Research Funds(DUT16LK40)for the Central Universities
文摘A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of P are lying in?;V and coplanar with J. In this paper, we show that the number of boundary components of spanning pre-disks in a compression body is unbounded. But the number of a maximal collection of spanning pre-disks is bounded.
