For any alternating prime knot [Formula: see text], it is expected that the canonical genus of its Whitehead double is equal to the crossing number of [Formula: see text]. We introduce local moves of alternating knots, and prove that these local moves preserve the canonical genus of its Whitehead double under a certain condition. By this result, we give a new family of knots which satisfy this conjecture.

中文翻译：

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其Whitehead双节交替结保留规范属的局部移动

对于任何交替素结[公式：见正文]，预计其怀特黑德替身的规范属等于[公式：见正文]的交叉数。我们引入交替结的局部移动，并证明这些局部移动在一定条件下保留了其怀特黑德替身的规范属。通过这个结果，我们给出了一个满足这个猜想的新的结族。