The head and tail conjecture for alternating knots
By Cody Armond. 2011
49 citations recorded by the source corpus.
We investigate the coefficients of the highest and lowest terms (also called the head and the tail) of the colored Jones polynomial and show that they stabilize for alternating links and for adequate links. To do this we apply techniques from skein theory.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/228dc1575254454533ce9324c66eb5cef14047d0
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial (2011, background): “ in general, e.g. for (negative) (p;q)-torus knots with p;q>2. The proof of the conjecture for all alternating links was recently completed and will be posted in a separate paper by the rst author [Arm11a]. We do not make use of this result here. We learned that independently, L^e and Garoufalidi”