Twisted alexander polynomials on curves in character varieties of knot groups

Taehee Kim, Takahiro Kitayama, Takayuki Morifuji

Research output: Contribution to journalReview article

4 Citations (Scopus)

Abstract

For a fibered knot in the 3-sphere the twisted Alexander polynomial associated to an SL(2)-character is known to be monic. It is conjectured that for a nonfibered knot there is a curve component of the SL(2)-character variety containing only finitely many characters whose twisted Alexander polynomials are monic, i.e. finiteness of such characters detects fiberedness of knots. In this paper, we discuss the existence of a certain curve component which relates to the conjecture when knots have nonmonic Alexander polynomials. We also discuss the similar problem of detecting the knot genus.

Original languageEnglish
Article number1350022
JournalInternational Journal of Mathematics
Volume24
Issue number3
DOIs
Publication statusPublished - 2013 Mar 1

Keywords

  • 57M05
  • 57M25
  • Twisted Alexander polynomial
  • character variety
  • fibered knot 57M27

ASJC Scopus subject areas

  • Mathematics(all)

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