We formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the twisted homology groups in a $\mathbb{Z}$-cover of a 3-manifold with use of Mahler measures. We examine several examples associated to Riley’s parabolic representations of two-bridge knot groups and give a remark on hyperbolic volumes.

中文翻译：

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扭曲的亚历山大多项式的无限刚度

我们为扭曲的亚历山大多项式拟定并证明了一个有限刚性定理，直至几种类型的有限歧义。我们还建立了一个扭曲的同源群体的扭转增长公式$\mathbb{Z}$-使用Mahler测度覆盖3个歧管。我们研究了与两个桥结组的莱利抛物线表示相关的几个示例，并给出了双曲线体积的说明。