Remarks on Jones slopes and surfaces of knots

2020/02/27 by Kalfagianni, Efstratia
#FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2002.12367

Abstract

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.

Related

• Normal and Jones surfaces of knots
• The Jones slopes of a knot
• Jones slopes and coarse volume of near-alternating links
• A slope conjecture for links
• The Slope Conjecture for Montesinos knots