On the universal sl_2 invariant of boundary bottom tangles

Sakie Suzuki

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arXiv · 1103.2204

On the universal sl_2 invariant of boundary bottom tangles

Sakie Suzuki

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Abstract

The universal sl_2 invariant of bottom tangles has a universality property for the colored Jones polynomial of links. Habiro conjectured that the universal sl_2 invariant of boundary bottom tangles takes values in certain subalgebras of the completed tensor powers of the quantized enveloping algebra U_h(sl_2) of the Lie algebra sl_2. In the present paper, we prove an improved version of Habiro's conjecture. As an application, we prove a divisibility property of the colored Jones polynomial of boundary links.

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Sakie Suzuki. 2011-03-11. On the universal sl_2 invariant of boundary bottom tangles. https://arxiv.org/abs/1103.2204

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