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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

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.

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knot theory, Jones polynomial, tail, Manx, stabilization
Mathematical Subject Classification
Primary: 57K10
Received: 9 December 2020
Revised: 28 April 2021
Accepted: 23 May 2021
Published: 13 December 2022
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