Twisted alexander polynomials on curves in character varieties of knot groups

Taehee Kim, Takahiro Kitayama, Takayuki Morifuji

研究成果: Review article査読

5 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号1350022
ジャーナルInternational Journal of Mathematics
24
3
DOI
出版ステータスPublished - 2013 3

ASJC Scopus subject areas

  • 数学 (全般)

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