论文标题
三倍数字，结或链接和圆环的属
Triple-crossing number, the genus of a knot or link and torus knots
论文作者
论文摘要
我们表明，任何结的三重打结的数量大或等于其（规范）属的两倍，并且在链接的情况下，我们显示出更强的结合。作为一个应用，我们表明这种结合足以获得所有圆环结的三重跨数字，以及更多的结及其连接的总和。
We show that the triple-crossing number of any knot is greater or equal to twice its (canonical) genus and we show an even stronger bound in the case of links. As an application we show that this bound is strong enough to obtain the triple-crossing numbers of all torus knots, and of many more knots and their connected sums.
