Twisted Alexander polynomials for irreducible SL(2,)-representations of torus knots
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 2, pp. 395-406.

We prove that the twisted Alexander polynomial of a torus knot with an irreducible SL(2,)-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.

Published online:
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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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, Serie 5, Volume 11 (2012) no. 2, pp. 395-406. http://archive.numdam.org/item/ASNSP_2012_5_11_2_395_0/

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