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/} }
TY - JOUR AU - Kitano, Teruaki AU - Morifuji, Takayuki TI - Twisted Alexander polynomials for irreducible $SL(2,\protect \mathbb{C})$-representations of torus knots JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 395 EP - 406 VL - 11 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_2_395_0/ LA - en ID - ASNSP_2012_5_11_2_395_0 ER -
%0 Journal Article %A Kitano, Teruaki %A Morifuji, Takayuki %T Twisted Alexander polynomials for irreducible $SL(2,\protect \mathbb{C})$-representations of torus knots %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 395-406 %V 11 %N 2 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_2_395_0/ %G en %F ASNSP_2012_5_11_2_395_0
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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