Colored Jones polynomials without tails

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.

5 pages, 1 cat

References in corpus (2)

• Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial
• A trivial tail homology for non $A$-adequate links