RIMS - 1671 On the universal sl 2 invariant of ribbon bottom tangles

A bottom tangle is a tangle in a cube consisting of arc components whose boundary points are on a line in the bottom square of the cube. A ribbon bottom tangle is a bottom tangle whose closure is a ribbon link. For every n-component ribbon bottom tangle T , we prove that the universal invariant JT of T associated to the quantized enveloping algebra Uh(sl2) of the Lie algebra sl2 is contained in a certain Z[q, q−1]subalgebra of the n-fold completed tensor power U ⊗̂n h (sl2) of Uh(sl2). This result is applied to the colored Jones polynomial of ribbon links.