Colored Jones polynomials without tails

Lee, Christine Ruey Shan; van der Veen, Roland

doi:10.2140/agt.2022.22.2857

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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

Mathematical Subject Classification

Primary: 57K10

References

Publication

Received: 9 December 2020

Revised: 28 April 2021

Accepted: 23 May 2021

Published: 13 December 2022

Authors

Christine Ruey Shan Lee
Department of Mathematics Texas State University San Marcos, TX United States

Roland van der Veen
Department of Mathematics Bernoulli Institute University of Groningen Groningen Netherlands

Volume 22, issue 6 (2022)