Algebraic & Geometric Topology 12 (2012) 997–1057

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 U_h(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.

Keywords

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

Mathematical Subject Classification

Primary: 57M27

Secondary: 57M25

References

Publication

Received: 2 April 2011
Revised: 1 February 2012
Accepted: 29 November 2011
Published: 7 May 2012

Authors