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FACTORIZATION FORMULAS AND COMPUTATIONS OF HIGHER-ORDER ALEXANDER INVARIANTS FOR HOMOLOGICALLY FIBERED KNOTS

Department of Mathematics, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, Tokyo 184-8588, Japan

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TAKUYA SAKASAI

Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan

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https://doi.org/10.1142/S0218216511009303Cited by:5 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 57M25, 57M27

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