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- Title
TWISTED ALEXANDER POLYNOMIALS ON CURVES IN CHARACTER VARIETIES OF KNOT GROUPS.
- Authors
KIM, TAEHEE; KITAYAMA, TAKAHIRO; MORIFUJI, TAKAYUKI
- Abstract
For a fibered knot in the 3-sphere the twisted Alexander polynomial associated to an SL(2, ℂ)-character is known to be monic. It is conjectured that for a nonfibered knot there is a curve component of the SL(2, ℂ)-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.
- Subjects
POLYNOMIALS; CURVES; VARIETIES (Universal algebra); KNOT groups; EXISTENCE theorems; MATHEMATICAL analysis; NUMERICAL analysis
- Publication
International Journal of Mathematics, 2013, Vol 24, Issue 3, p-1
- ISSN
0129-167X
- Publication type
Article
- DOI
10.1142/S0129167X13500225