Stability properties of the colored Jones polynomial.

It is known that the colored Jones polynomial of a + -adequate link has a well-defined tail consisting of stable coefficients, and that the coefficients of the tail carry geometric and topological information on the + -adequate link complement. We show that a power series similar to the tail of the colored Jones polynomial for + -adequate links can be defined for all links, and that it is trivial if and only if the link is non + -adequate. [ABSTRACT FROM AUTHOR]