Divisibility of twisted Alexander polynomials and fibered knots
Kitano, Teruaki1 ; Morifuji, Takayuki2
1 Department of Mathematical and Computing Sciences Tokyo Institute of Technology 2-12-1-W8-43 Oh-okayama, Meguro-ku Tokyo 152-8552, Japan
2 Department of Mathematics Tokyo University of Agriculture and Technology 2-24-16 Naka-cho, Koganei Tokyo 184-8588, Japan
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 1, pp. 179-186.

We prove that Wada’s twisted Alexander polynomial of a knot group associated to any nonabelian SL(2,𝔽)-representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree 4g-2 for a fibered knot of genus g.

Classification : 57M25, 57M05
Kitano, Teruaki 1 ; Morifuji, Takayuki 2

1 Department of Mathematical and Computing Sciences Tokyo Institute of Technology 2-12-1-W8-43 Oh-okayama, Meguro-ku Tokyo 152-8552, Japan
2 Department of Mathematics Tokyo University of Agriculture and Technology 2-24-16 Naka-cho, Koganei Tokyo 184-8588, Japan 
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Kitano, Teruaki; Morifuji, Takayuki. Divisibility of twisted Alexander polynomials and fibered knots. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 1, pp. 179-186. http://www.numdam.org/item/ASNSP_2005_5_4_1_179_0/

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