For any nonorientable closed surface, we determine the minimal dilatation among pseudo-Anosov mapping classes arising from Penner’s construction. We deduce that the sequence of minimal Penner dilatations has exactly two accumulation points, in contrast to the case of orientable surfaces where there is only one accumulation point. One of our key techniques is representing pseudo-Anosov dilatations as roots of Alexander polynomials of fibered links and comparing dilatations using the skein relation for Alexander polynomials.

中文翻译：

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不可定向表面上的最小彭纳膨胀

对于任何不可定向的闭合曲面，我们确定由 Penner 构造产生的伪阿诺索夫映射类之间的最小膨胀。我们推断最小 Penner 膨胀序列恰好有两个累积点，这与只有一个累积点的可定向表面的情况形成对比。我们的一项关键技术是将伪阿诺索夫膨胀表示为光纤链接的亚历山大多项式的根，并使用亚历山大多项式的绞线关系比较膨胀。