Any knot $K$ in genus-1 1-bridge position can be moved by isotopy to lie in a union of $n$ parallel tori tubed by $n-1$ tubes so that $K$ intersects each tube in two spanning arcs, which we call a leveling of the position. The minimal $n$ for which this is possible is an invariant of the position, called the level number. In this work, we describe the leveling by the braid group on two points in the torus, which yields a numerical invariant of the position, called the (1, 1)-length. We show that the (1, 1)-length equals the level number. We then find braid descriptions for (1,1)-positions of all 2-bridge knots providing upper bounds for their level numbers and also show that the (-2, 3, 7)-pretzel knot has level number two.

任何结$钾$在 genus-1 中，1 桥位置可以通过同位素移动以位于联合中$n$平行圆环由$n-\mathrm{1个}$管这样$钾$以两个跨越弧线与每个管相交，我们称之为平整位置。最小的$n$这是可能的是位置的不变量，称为级别数。在这项工作中，我们描述了环面中两点上编织群的拉平，这产生了位置的数值不变量，称为 (1, 1)-length。我们表明 (1, 1)-length 等于级别数。然后，我们找到所有 2 桥结的 (1,1)-位置的编织描述，为其级别数提供上限，并且还表明 (-2, 3, 7)-pretzel 结具有第二级。