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On the universal sl_2 invariant of boundary bottom tangles

By Sakie Suzuki

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

Topics: Mathematics - Geometric Topology, Mathematics - Quantum Algebra, 57M27, 57M25
Year: 2011
OAI identifier: oai:arXiv.org:1103.2204
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