Factorization formulas and computations of higher-order alexander invariants for homologically fibered knots

摘要

Homologically fibered knots are knots whose exteriors satisfy the same homological conditions as fibered knots. In our previous paper, we observed that for such a knot, higher-order Alexander invariants defined by Cochran, Harvey, and Friedl are generally factorized into the part of the Magnus matrix and that of a certain Reidemeister torsion, both of which are known as invariants of homology cylinders over a surface. In this paper, we study more details of the invariants and give their concrete calculations after restricting to the case of the invariants associated with metabelian quotients of knot groups. We provide explicit computational results of the invariants for all the 12-crossings non-fibered homologically fibered knots.