Twisted alexander polynomials and character varieties of 2-bridge knot groups

Taehee Kim, Takayuki Morifuji

Research output: Contribution to journalReview article

9 Citations (Scopus)

Abstract

We study the twisted Alexander polynomial from the viewpoint of the SL(2,&Cmathbb;)-character variety of nonabelian representations of a knot group. It is known that if a knot is fibered, then the twisted Alexander polynomials associated with nonabelian SL(2,&Cmathbb;)-representations are all monic. In this paper, we show that for a 2-bridge knot there exists a curve component in the SL(2,&Cmathbb;)-character variety such that if the knot is not fibered then there are only finitely many characters in the component for which the associated twisted Alexander polynomials are monic. We also show that for a 2-bridge knot of genus g, in the above curve component for all but finitely many characters the associated twisted Alexander polynomials have degree 4g - 2.

Original languageEnglish
Article number1250022
JournalInternational Journal of Mathematics
Volume23
Issue number6
DOIs
Publication statusPublished - 2012 Jun 1

Keywords

  • 2-bridge knot
  • Twisted Alexander polynomial
  • character variety

ASJC Scopus subject areas

  • Mathematics(all)

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