On the universal sl2 invariant of boundary bottom tangles

Suzuki, Sakie

doi:10.2140/agt.2012.12.997

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On the universal $sl_2$ invariant of boundary bottom tangles

Sakie Suzuki

Algebraic & Geometric Topology 12 (2012) 997–1057

DOI: 10.2140/agt.2012.12.997

Abstract

The universal $s l_{2}$ 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 $s l_{2}$ invariant of boundary bottom tangles takes values in certain subalgebras of the completed tensor powers of the quantized enveloping algebra $U_{h} (s l_{2})$ of the Lie algebra $s l_{2}$ . 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.

Keywords

quantum invariant, universal invariant, colored Jones polynomial, boundary link, bottom tangle

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 57M25

References

Publication

Received: 2 April 2011

Revised: 1 February 2012

Accepted: 29 November 2011

Published: 7 May 2012

Authors

Sakie Suzuki
Research Institute for Mathematical Sciences Kyoto University Kyoto 606-8502 Japan
http://www.kurims.kyoto-u.ac.jp/~sakie/

Volume 12, issue 2 (2012)