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Volume 34, Issue 2
Weakly Disk-Busting Curves in the Boundary of a Compression Body

Meng Sun & Liang Liang

DOI: 10.13447/j.1674-5647.2018.02.09

Commun. Math. Res., 34 (2018), pp. 171-176.

Published online: 2019-12

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  • Abstract

Let $V$ be a nontrivial compression body which is not simple. An essential simple closed curve $J$ in $\partial_+V$ is called weakly disk-busting if $\partial_+V-J$ 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.

  • Keywords

handle addition, curve complex, subsurface projection, weakly disk-busting

  • AMS Subject Headings

57N10, 57M50

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

13904801741@163.com (Meng Sun)

liang_liang@aliyun.com (Liang Liang)

  • BibTex
  • RIS
  • TXT
@Article{CMR-34-171, author = {Sun , Meng and Liang , Liang}, title = {Weakly Disk-Busting Curves in the Boundary of a Compression Body}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {2}, pages = {171--176}, abstract = {

Let $V$ be a nontrivial compression body which is not simple. An essential simple closed curve $J$ in $\partial_+V$ is called weakly disk-busting if $\partial_+V-J$ 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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.02.09}, url = {http://global-sci.org/intro/article_detail/cmr/13524.html} }
TY - JOUR T1 - Weakly Disk-Busting Curves in the Boundary of a Compression Body AU - Sun , Meng AU - Liang , Liang JO - Communications in Mathematical Research VL - 2 SP - 171 EP - 176 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.02.09 UR - https://global-sci.org/intro/article_detail/cmr/13524.html KW - handle addition, curve complex, subsurface projection, weakly disk-busting AB -

Let $V$ be a nontrivial compression body which is not simple. An essential simple closed curve $J$ in $\partial_+V$ is called weakly disk-busting if $\partial_+V-J$ 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.

Sun , Meng and Liang , Liang. (2019). Weakly Disk-Busting Curves in the Boundary of a Compression Body. Communications in Mathematical Research . 34 (2). 171-176. doi:10.13447/j.1674-5647.2018.02.09
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