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 - <p style="text-align: justify;">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.</p>