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

Liang Liang, Youfa Han, Fengling Li & Luying Zhao

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

Published online: 2019-12

Preview Purchase PDF 57 2930
Export citation
  • 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

  • AMS Subject Headings

57N10, 57M50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

liang_liang@aliyun.com (Liang Liang)

  • BibTex
  • RIS
  • TXT
@Article{CMR-34-177, author = {Liang , Liang and Han , Youfa and Li , Fengling and Zhao , Luying}, 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
Copy to clipboard
The citation has been copied to your clipboard