We prove that the twisted Alexander polynomial of a torus knot with an irreducible -representation is locally constant. In the case of a 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.
@article{ASNSP_2012_5_11_2_395_0,
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},
zbl = {1255.57014},
mrnumber = {3011996},
language = {en},
url = {http://archive.numdam.org/item/ASNSP_2012_5_11_2_395_0/}
}
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AU - Kitano, Teruaki
AU - Morifuji, Takayuki
TI - Twisted Alexander polynomials for irreducible $SL(2,\protect \mathbb{C})$-representations of torus knots
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PY - 2012
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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://archive.numdam.org/item/ASNSP_2012_5_11_2_395_0/
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