Colored alexander invariants and cone-manifolds

In this paper, we reconstruct the link invariant of framed links introduced in [1] by the universal R-matrix of U_q(sl₂) and name it the colored Alexander invariant. We check that the optimistic limit o-lim of this invariant is determined by the volume of the knot and link cone-manifold for figure eight knot, Whitehead link and Borromean rings. We also propose the A-polynomials of these examples obtained from the colored Alexander invariant.