Divisibility of twisted Alexander polynomials and fibered knots

Kitano, Teruaki; Morifuji, Takayuki

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

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 4 (2005) no. 1, pp. 179-186.

Résumé

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

MR Zbl | 1 citation dans Numdam

Classification : 57M25, 57M05

Affiliations des auteurs :

Kitano, Teruaki ¹ ; Morifuji, Takayuki ²

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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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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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