Year: 2013
Author: Dongqi Sun, Jingyan Tang, Fengling Li
Communications in Mathematical Research , Vol. 29 (2013), Iss. 2 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-CMR-19022
Communications in Mathematical Research , Vol. 29 (2013), Iss. 2 : pp. 184–192
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: handlebody planar surface planar-busting curve pants-busting curve.