曲面纽结的交变

摘要：

本文讨论了曲面纽结图的可交换双曲线的交换运算。证明了在一定条件下，一个有限序列的Roseman移动保持可交换双曲线的性质。作为这一结果的应用，我们还定义了一个数值不变量的一组表面的结称为$du$ -可交换集。

英文摘要：

In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called $du$-exchangeable set.

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