Geodesic
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

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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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     title = {Divisibility of twisted {Alexander} polynomials and fibered knots},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {179--186},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 4},
     number = {1},
     year = {2005},
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     zbl = {1117.57004},
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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://geodesic.mathdoc.fr/item/ASNSP_2005_5_4_1_179_0/