Volume 12, issue 2 (2012)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17, 1 issue

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On the universal $sl_2$ invariant of boundary bottom tangles

Sakie Suzuki

Algebraic & Geometric Topology 12 (2012) 997–1057

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.

quantum invariant, universal invariant, colored Jones polynomial, boundary link, bottom tangle
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25
Received: 2 April 2011
Revised: 1 February 2012
Accepted: 29 November 2011
Published: 7 May 2012
Sakie Suzuki
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502