Volume 10, issue 2 (2010)

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

Volume 14
Issue 5, 2511–3139
Issue 4, 1881–2509
Issue 3, 1249–1879
Issue 2, 627–1247
Issue 1, 1–625

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
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On the universal $sl_2$ invariant of ribbon bottom tangles

Sakie Suzuki

Algebraic & Geometric Topology 10 (2010) 1027–1061
Abstract

A bottom tangle is a tangle in a cube consisting of arc components whose boundary points are placed on the bottom, and every link can be represented as the closure of a bottom tangle. The universal sl2 invariant of n–component bottom tangles takes values in the n–fold completed tensor power of the quantized enveloping algebra Uh(sl2), and has a universality property for the colored Jones polynomials of n–component links via quantum traces in finite dimensional representations. In the present paper, we prove that if the closure of a bottom tangle T is a ribbon link, then the universal sl2 invariant of T is contained in a certain small subalgebra of the completed tensor power of Uh(sl2). As an application, we prove that ribbon links have stronger divisibility by cyclotomic polynomials than algebraically split links for Habiro’s reduced version of the colored Jones polynomials.

Keywords
bottom tangle, boundary bottom tangle, boundary link, universal $sl_2$ invariant, colored Jones polynomial
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25
References
Publication
Received: 29 May 2009
Accepted: 12 January 2010
Published: 26 April 2010
Authors
Sakie Suzuki
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502
Japan
http://www.kurims.kyoto-u.ac.jp/~sakie/