Twisted Alexander polynomials for SL(2;C)-irreducible representations of torus knots

• Teruaki Kitano ^[1] ; Takayuki Morifuji ^[2]
  1. [1] Soka University

     Soka University

     Japón

     
  2. [2] Keio University

     Keio University

     Japón

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 11, Nº 2, 2012, págs. 395-406
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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.