Geodesic
Twisted Alexander polynomials for irreducible SL(2,ℂ)-representations of torus knots
Kitano, Teruaki1 ; Morifuji, Takayuki2
1 Department of Information Systems Science, Faculty of Engineering Soka University Tangi-cho 1-236 Hachioji, Tokyo 192-8577, Japan
2 Department of Mathematics Hiyoshi Campus Keio University Yokohama 223-8521, Japan
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 2, pp. 395-406

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We prove that the twisted Alexander polynomial of a torus knot with an irreducible SL(2,ℂ)-representation is locally constant. In the case of a (2,q) torus knot, we can give an explicit formula for the twisted Alexander polynomial and deduce Hirasawa-Murasugi’s formula for the total twisted Alexander polynomial. We also give examples which address a mis-statement in a paper of Silver and Williams.

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Classification : 57M27

Kitano, Teruaki 1 ; Morifuji, Takayuki 2

1 Department of Information Systems Science, Faculty of Engineering Soka University Tangi-cho 1-236 Hachioji, Tokyo 192-8577, Japan
2 Department of Mathematics Hiyoshi Campus Keio University Yokohama 223-8521, Japan 
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     author = {Kitano, Teruaki and Morifuji, Takayuki},
     title = {Twisted {Alexander} polynomials for irreducible $SL(2,\protect \mathbb{C})$-representations of torus knots},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {395--406},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 11},
     number = {2},
     year = {2012},
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     mrnumber = {3011996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_2_395_0/}
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Kitano, Teruaki; Morifuji, Takayuki. Twisted Alexander polynomials for irreducible $SL(2,\protect \mathbb{C})$-representations of torus knots. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 11 (2012) no. 2, pp. 395-406. http://geodesic.mathdoc.fr/item/ASNSP_2012_5_11_2_395_0/