A volume-ish theorem for the Jones polynomial
preprint available here
of alternating knots.
The Volume conjecture claims that
the
hyperbolic Volume of a knot is
determined by the colored Jones polynomial.
The purpose of this article is to show a Volume-ish theorem for
alternating
knots in terms of the Jones polynomial, rather than the colored Jones
polynomial: The ratio of the Volume and certain sums of coefficients of
the
Jones polynomial is bounded from above and from below by constants.
Furthermore, we give experimental data on the relation of the growths
of
the
hyperbolic volume and the coefficients of the Jones polynomial, both
for alternating and non-alternating knots.
Jones Polynomial, Volume Conjecture, Alternating Knots, Tutte Polynomial