Given an oriented minimal genus Seifert surface F′ for a (1, 1)-knot K it is possible to surger F′ along annuli to obtain a simple minimal Seifert surfaceF . Such a surface can be put in a very nice position with respect to the (1, 1)-position of the knot K. Using this kind of surfaces we give a description of a (1, 1)-knot of genus g as a vertical banding of (1, 1)-knots of genus smaller than g. In addition, we show that any rational knot of genus g is obtained as a vertical banding of g genus one rational knots.

中文翻译：

---

关于承认 (1,1)-分解的 g 类结的分类

给定一个有向的最小属 Seifert 曲面F'为一个(1, 1)-结ķ可以手术F'沿着环形获得一个简单的最小 Seifert 曲面F . 这样的表面可以相对于(1, 1)- 结的位置ķ. 使用这种表面，我们给出了一个描述(1, 1)- 属结G作为垂直条带(1, 1)- 属节小于G. 此外，我们证明了任何有理的属结G作为垂直条带获得G属一有理结。