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2012 On the universal $sl_2$ invariant of boundary bottom tangles
Sakie Suzuki
Algebr. Geom. Topol. 12(2): 997-1057 (2012). DOI: 10.2140/agt.2012.12.997

Abstract

The universal sl2 invariant of bottom tangles has a universality property for the colored Jones polynomial of links. A bottom tangle is called boundary if its components admit mutually disjoint Seifert surfaces. Habiro conjectured that the universal sl2 invariant of boundary bottom tangles takes values in certain subalgebras of the completed tensor powers of the quantized enveloping algebra Uh(sl2) of the Lie algebra sl2. 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. "On the universal $sl_2$ invariant of boundary bottom tangles." Algebr. Geom. Topol. 12 (2) 997 - 1057, 2012. https://doi.org/10.2140/agt.2012.12.997

Information

Received: 2 April 2011; Revised: 1 February 2012; Accepted: 29 November 2011; Published: 2012
First available in Project Euclid: 19 December 2017

zbMATH: 1246.57027
MathSciNet: MR2928903
Digital Object Identifier: 10.2140/agt.2012.12.997

Subjects:
Primary: 57M27
Secondary: 57M25

Rights: Copyright © 2012 Mathematical Sciences Publishers

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Vol.12 • No. 2 • 2012
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