On the universal sl_2 invariant of ribbon bottom tangles

Details On the universal sl_2 invariant of ribbon bottom tangles On the universal sl_2 invariant of ribbon bottom tangles

2009-05-12

arxiv.org/abs/0905.1783v1

Mathematics

Geometric Topology

Scientific paper

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 J_T of T associated to the quantized enveloping algebra U_h(sl_2) of the Lie algebra sl_2 is contained in a certain Z[q,q^{-1}]-subalgebra of the n-fold completed tensor power of U_h(sl_2). This result is applied to the colored Jones polynomial of ribbon links.

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