Volume 5, issue 4 (2005)

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

Volume 23
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Hopf diagrams and quantum invariants

Alain Bruguieres and Alexis Virelizier

Algebraic & Geometric Topology 5 (2005) 1677–1710

arXiv: math.QA/0505119

Abstract

The Reshetikhin–Turaev invariant, Turaev’s TQFT, and many related constructions rely on the encoding of certain tangles (n–string links, or ribbon n–handles) as n–forms on the coend of a ribbon category. We introduce the monoidal category of Hopf diagrams, and describe a universal encoding of ribbon string links as Hopf diagrams. This universal encoding is an injective monoidal functor and admits a straightforward monoidal retraction. Any Hopf diagram with n legs yields a n–form on the coend of a ribbon category in a completely explicit way. Thus computing a quantum invariant of a 3–manifold reduces to the purely formal computation of the associated Hopf diagram, followed by the evaluation of this diagram in a given category (using in particular the so-called Kirby elements).

Keywords
Hopf diagrams, string links, quantum invariants
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 18D10, 81R50
References
Forward citations
Publication
Received: 13 June 2005
Accepted: 28 November 2005
Published: 7 December 2005
Authors
Alain Bruguieres
I3M
Université Montpellier II
34095 Montpellier Cedex 5
France
Alexis Virelizier
Department of Mathematics
University of California
Berkeley CA 94720
USA