The head and tail conjecture for alternating knots

Cody Armond

Type: Article

Publication Date: 2013-07-18

Citations: 54

DOI: https://doi.org/10.2140/agt.2013.13.2809

Abstract

The head and tail conjecture for alternating knots CODY ARMONDWe 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.

Locations

Algebraic & Geometric Topology - View - PDF
arXiv (Cornell University) - View - PDF
Project Euclid (Cornell University) - View - PDF
LSU Digital Commons (Louisiana State University) - View - PDF
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+ PDF Chat	Coloured $$\mathfrak {sl}_r$$ invariants of torus knots and characters of $${\mathcal {W}}_r$$ algebras	2023	Shashank Kanade
+	Nahm sums, stability and the colored Jones polynomial	2011	Stavros Garoufalidis Thang T. Q. Lê
+	Quantum knot invariants	2018	Stavros Garoufalidis
+	Flag algebras and the stable coefficients of the Jones polynomial	2013	Stavros Garoufalidis Sergey Norin Thao Vuong
+	Alternating knots, planar graphs and q-series	2013	Stavros Garoufalidis Thao Vuong
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Works Cited by This (7)

Action	Title	Year	Authors
+	Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial	2011	Cody Armond Oliver T. Dasbach
+ PDF Chat	Nahm sums, stability and the colored Jones polynomial	2015	Stavros Garoufalidis Thang T. Q. Lê
+ PDF Chat	A volumish theorem for the Jones polynomial of alternating knots	2007	Oliver T. Dasbach Xiao-Song Lin
+ PDF Chat	3-valent graphs and the Kauffman bracket	1994	Gregor Masbaum Pierre Vogel
+	On the tail of Jones polynomials of closed braids with a full twist	2013	Abhijit Champanerkar Ilya Kofman
+	An Introduction to Knot Theory	1997	W. B. R. Lickorish
+ PDF Chat	On the head and the tail of the colored Jones polynomial	2006	Oliver T. Dasbach Xiao-Song Lin