Volume 5, issue 4 (2005)

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

Volume 20
Issue 7, 3219–3760
Issue 6, 2687–3218
Issue 5, 2145–2685
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

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