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Colored Jones polynomials without tails

### Christine Ruey Shan Lee and Roland van der Veen

Algebraic & Geometric Topology 22 (2022) 2857–2865
DOI: 10.2140/agt.2022.22.2857
##### Abstract

We exhibit an infinite family of knots with the property that the first coefficient of the $n$–colored Jones polynomial grows linearly with $n$. This shows that the concept of stability and tail seen in the colored Jones polynomials of alternating knots does not generalize naively.

##### Keywords
knot theory, Jones polynomial, tail, Manx, stabilization
Primary: 57K10