Let Hn 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 δHm. In the present paper, we prove that for n not less than 2, there exists an e...Let Hn 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 δHm. In the present paper, we prove that for n not less than 2, there exists an essential simple closed curve C in OHm which intersects each essential planar surface in Hn non-emptily. Furthermore, we show that for n not less than 3, a pants-busting curve must also be an annulus-busting curve.展开更多
基金The grant (09XBKQ09) of Harbin Normal Universitythe NSF (11101058) of ChinaChina Postdoctoral Science Foundation (2011M500049)
文摘Let Hn 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 δHm. In the present paper, we prove that for n not less than 2, there exists an essential simple closed curve C in OHm which intersects each essential planar surface in Hn non-emptily. Furthermore, we show that for n not less than 3, a pants-busting curve must also be an annulus-busting curve.
