Remarks on Jones slopes and surfaces of knots
We point out that the strong slope conjecture implies that the degrees of the colored Jones knot polynomials detect the figure eight knot. Furthermore, we propose a characterization of alternating knots in terms of the Jones period and the degree span of the colored Jones polynomial.
Authors:
Award ID(s):
Publication Date:
NSF-PAR ID:
10233272
Journal Name:
Acta mathematica Vietnamica
Volume:
46
Issue:
2
Page Range or eLocation-ID:
289–299
ISSN:
2315-4144
1. We observe that the strong slope conjecture implies that the degree of the colored Jones polynomial detects all torus knots. As an application we obtain that an adequate knot that has the same colored Jones polynomial degrees as a torus knot must be a $(2,q)$-torus knot.