论文标题
纤维的刚性刚度
Profinite rigidity of fibring
论文作者
论文摘要
我们介绍了TAP组的类别，在这些类别中，通过非扭曲的Alexander多项式来检测到各种类型的代数纤维。我们表明，有限呈现的LERF组位于每个积分域$ r $的类$ \ mathsf {tap} _1（r）$中，并推断出代数纤维是此类群体的Profinite属性。我们为限制组产品的代数纤维以及对庞加莱二元组的刚性刚度的应用提供了更强的结果。
We introduce the classes of TAP groups, in which various types of algebraic fibring are detected by the non-vanishing of twisted Alexander polynomials. We show that finitely presented LERF groups lie in the class $\mathsf{TAP}_1(R)$ for every integral domain $R$, and deduce that algebraic fibring is a profinite property for such groups. We offer stronger results for algebraic fibring of products of limit groups, as well as applications to profinite rigidity of Poincaré duality groups in dimension $3$ and RFRS groups.
