Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-20T14:28:49.207Z Has data issue: false hasContentIssue false
  • English
  • Français

On the head and the tail of the colored Jones polynomial

Published online by Cambridge University Press:  25 September 2006

Oliver T. Dasbach  and
Xiao-Song Lin
Oliver T. Dasbach
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, [email protected]
Xiao-Song Lin
Affiliation:
Department of Mathematics, University of California, Riverside, CA 92521, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The colored Jones polynomial is a function $J_K:{\mathbb{N}}\longrightarrow{\mathbb{Z}}[t,t^{-1}]$ associated with a knot $K$ in 3-space. We will show that for an alternating knot $K$ the absolute values of the first and the last three leading coefficients of $J_K(n)$ are independent of $n$ when $n$ is sufficiently large. Computation of sample knots indicates that this should be true for any fixed leading coefficient of the colored Jones polynomial for alternating knots. As a corollary we get a volume-ish theorem for the colored Jones polynomial.

Keywords

colored Jones polynomialvolume-ish theoremvolume conjecture57M25
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 5 , September 2006 , pp. 1332 - 1342
Copyright
Foundation Compositio Mathematica 2006