Homology Groups and Ideal Class Groups III: Asymptotic Formulas

As we discussed in Chap. 10 , there is a group-theoretic analogy between the knot module associated to the infinite cyclic covering of a knot exterior and the Iwasawa module associated to the cyclotomic \(\mathbb {Z}_p\) -extension of number fields. Based on this analogy, there are found close parallels between the Alexander–Fox theory and Iwasawa theory.