Volume 34, Issue 2
Spanning Pre-Disks in a Compression Body

Commun. Math. Res., 34 (2018), pp. 177-183.

Published online: 2019-12

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• 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.

• Keywords

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

57N10, 57M50

liang_liang@aliyun.com (Liang Liang)

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@Article{CMR-34-177, author = {Liang and Liang and liang_liang@aliyun.com and 6012 and School of Mathematics, Liaoning Normal University, Dalian, Liaoning, 116029 and Liang Liang and Youfa and Han and and 6013 and School of Mathematics, Liaoning Normal University, Dalian, Liaoning, 116029 and Youfa Han and Fengling and Li and and 5416 and School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024 and Fengling Li and Luying and Zhao and and 6014 and School of Mathematics, Liaoning Normal University, Dalian, Liaoning, 116029 and Luying Zhao}, title = {Spanning Pre-Disks in a Compression Body}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {2}, pages = {177--183}, 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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.02.10}, url = {http://global-sci.org/intro/article_detail/cmr/13522.html} }
TY - JOUR T1 - Spanning Pre-Disks in a Compression Body AU - Liang , Liang AU - Han , Youfa AU - Li , Fengling AU - Zhao , Luying JO - Communications in Mathematical Research VL - 2 SP - 177 EP - 183 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.02.10 UR - https://global-sci.org/intro/article_detail/cmr/13522.html KW - spanning pre-disk, curve complex, compression body, maximal collection AB -

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.

Liang Liang, Youfa Han, Fengling Li & Luying Zhao. (2019). Spanning Pre-Disks in a Compression Body. Communications in Mathematical Research . 34 (2). 177-183. doi:10.13447/j.1674-5647.2018.02.10
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