The Head and Tail of the Colored Jones Polynomial for Adequate Knots

2013/10/16 by Oliver T. Dasbach, Dasbach, Oliver T., Cody Armond +1 · 2 citations
Mathematics · #57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57M27

paper · pdf · doi:10.48550/arxiv.1310.4537

11 pages, 9 figures. arXiv admin note: text overlap with arXiv:1112.3995

arxiv created 2013/10/16 · arxiv updated 2013/10/18

Abstract

We show that the head and tail functions of the colored Jones polynomial of adequate links are the product of head and tail functions of the colored Jones polynomial of alternating links that can be read-off an adequate diagram of the link. We apply this to strengthen a theorem of Kalfagianni, Futer and Purcell on the fiberedness of adequate links.

Cited by

• A characterization of adequate Turaev genus one links
• Arborescent links and modular tails

Related

• Stability properties of the colored Jones polynomial
• On the head and the tail of the colored Jones polynomial
• On the degree of the colored Jones polynomial
• The head and tail conjecture for alternating knots
• Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial