On the head and the tail of the colored Jones polynomial

[摘要] 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.

[学科分类] 数学（综合）