Volume 29, Issue 2
Planar-Busting Curves on the Boundary of a Handlebody

Commun. Math. Res., 29 (2013), pp. 184-192.

Published online: 2021-05

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• Abstract

Let $H_n$ be an orientable handlebody of genus $n$. It has been proved that for $n$ not less than 2, there exists an annulus-busting curve in $∂H_n$. In the present paper, we prove that for $n$ not less than 2, there exists an essential simple closed curve $C$ in $∂H_n$ which intersects each essential planar surface in $H_n$ non-emptily. Furthermore, we show that for $n$ not less than 3, a pants-busting curve must also be an annulus-busting curve.

• Keywords

handlebody, planar surface, planar-busting curve, pants-busting curve.

57M99

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@Article{CMR-29-184, author = {Sun , DongqiTang , Jingyan and Li , Fengling}, title = {Planar-Busting Curves on the Boundary of a Handlebody}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {29}, number = {2}, pages = {184--192}, abstract = {

Let $H_n$ be an orientable handlebody of genus $n$. It has been proved that for $n$ not less than 2, there exists an annulus-busting curve in $∂H_n$. In the present paper, we prove that for $n$ not less than 2, there exists an essential simple closed curve $C$ in $∂H_n$ which intersects each essential planar surface in $H_n$ non-emptily. Furthermore, we show that for $n$ not less than 3, a pants-busting curve must also be an annulus-busting curve.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19022.html} }
TY - JOUR T1 - Planar-Busting Curves on the Boundary of a Handlebody AU - Sun , Dongqi AU - Tang , Jingyan AU - Li , Fengling JO - Communications in Mathematical Research VL - 2 SP - 184 EP - 192 PY - 2021 DA - 2021/05 SN - 29 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19022.html KW - handlebody, planar surface, planar-busting curve, pants-busting curve. AB -

Let $H_n$ be an orientable handlebody of genus $n$. It has been proved that for $n$ not less than 2, there exists an annulus-busting curve in $∂H_n$. In the present paper, we prove that for $n$ not less than 2, there exists an essential simple closed curve $C$ in $∂H_n$ which intersects each essential planar surface in $H_n$ non-emptily. Furthermore, we show that for $n$ not less than 3, a pants-busting curve must also be an annulus-busting curve.

Dongqi Sun, Jingyan Tang & Fengling Li. (2021). Planar-Busting Curves on the Boundary of a Handlebody. Communications in Mathematical Research . 29 (2). 184-192. doi:
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