From colored Jones invariants to logarithmic invariants

Abstract

In this work, we give a formula for the logarithmic invariant of knots in terms of certain derivatives of the colored Jones invariant. This invariant is related to the logarithmic conformal field theory, and was defined by using the centers in the radical of the restricted quantum group at root of unity. A relation between logarithmic invariant and the hyperbolic volume of a cone manifold is also investigated.