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A bottom tangle is a tangle in a cube consisting of arc components whose boundary
points are placed on the bottom, and every link can be represented as the closure of a
bottom tangle. The universal sl2 invariant of n–component bottom tangles takes
values in the n–fold completed tensor power of the quantized enveloping algebra
Uh(sl2), and has a universality property for the colored Jones polynomials of
n–component links via quantum traces in finite dimensional representations. In the
present paper, we prove that if the closure of a bottom tangle T is a ribbon
link, then the universal sl2 invariant of T is contained in a certain small
subalgebra of the completed tensor power of Uh(sl2). As an application, we prove
that ribbon links have stronger divisibility by cyclotomic polynomials than
algebraically split links for Habiro’s reduced version of the colored Jones
polynomials.
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