Commentarii Mathematici Helvetici


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Volume 80, Issue 1, 2005, pp. 51–61
DOI: 10.4171/CMH/3

Reidemeister torsion, twisted Alexander polynomial and fibered knots

Hiroshi Goda[1], TERUAKI KITANO[2] and Takayuki Morifuji[3]

(1) Department of Mathematics, Tokyo University of Agriculture and Technology, 2-24-16 NAKA-CHO, KOGANEI, 184-8588, TOKYO, JAPAN
(2) DEPARTMENT OF MATHEMATICAL AND COMPUTING SCIENCES, TOKYO INSTITUTE OF TECHNOLOGY, OOKAYAMA 2-12-1, MEGURO-KU, 152-8552, TOKYO, JAPAN
(3) Department of Mathematics, Tokyo University of Agriculture and Technology, 2-24-16 Naka-cho, Koganei, 184-8588, TOKYO, JAPAN

As a generalization of a classical result on the Alexander polynomial for fibered knots, we show in this paper that the Reidemeister torsion associated to a certain representation detects fiberedness of knots in the three sphere.

Keywords: Reidemeister torsion, twisted Alexander polynomial, fibered knot, representation.

Goda H, KITANO T, Morifuji T. Reidemeister torsion, twisted Alexander polynomial and fibered knots. Comment. Math. Helv. 80 (2005), 51-61. doi: 10.4171/CMH/3