Spanning Pre-Disks in a Compression Body

Authors

  • Liang Liang School of Mathematics, Liaoning Normal University, Dalian, Liaoning, 116029
  • Youfa Han School of Mathematics, Liaoning Normal University, Dalian, Liaoning, 116029
  • Fengling Li School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024
  • Luying Zhao School of Mathematics, Liaoning Normal University, Dalian, Liaoning, 116029

DOI:

https://doi.org/10.13447/j.1674-5647.2018.02.10

Keywords:

spanning pre-disk, curve complex, compression body, maximal collection

Abstract

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 $\partial_+V$ and all other boundary components of $P$ are lying in $\partial_-V$ 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.

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Published

2019-12-16

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Issue

Vol. 34 No. 2 (2018)

Section

Articles

How to Cite

Spanning Pre-Disks in a Compression Body. (2019). Communications in Mathematical Research, 34(2), 177-183. https://doi.org/10.13447/j.1674-5647.2018.02.10