On the universal sl_2 invariant of ribbon bottom tangles
Geometric Topology
2014-10-01 v1 Quantum Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.0905.1783,
title = {On the universal sl_2 invariant of ribbon bottom tangles},
author = {Sakie Suzuki},
journal= {arXiv preprint arXiv:0905.1783},
year = {2014}
}