Volume 5, issue 3 (2005)

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

Volume 14
Issue 6, 3141–3763
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
G&T Publications
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Skein theory for $SU(n)$–quantum invariants

Adam S Sikora

Algebraic & Geometric Topology 5 (2005) 865–897

arXiv: math.QA/0407299


For any n 2 we define an isotopy invariant, Γn, for a certain set of n–valent ribbon graphs Γ in 3, including all framed oriented links. We show that our bracket coincides with the Kauffman bracket for n = 2 and with the Kuperberg’s bracket for n = 3. Furthermore, we prove that for any n, our bracket of a link L is equal, up to normalization, to the SUn–quantum invariant of L. We show a number of properties of our bracket extending those of the Kauffman’s and Kuperberg’s brackets, and we relate it to the bracket of Murakami-Ohtsuki-Yamada. Finally, on the basis of the skein relations satisfied by n, we define the SUn–skein module of any 3–manifold M and we prove that it determines the SLn–character variety of π1(M).

Kauffman bracket, Kuperberg bracket, Murakami–Ohtsuki–Yamada bracket, quantum invariant, skein module
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 17B37
Forward citations
Received: 23 July 2004
Accepted: 9 May 2005
Published: 29 July 2005
Adam S Sikora
Department of Mathematics
University at Buffalo
Buffalo NY 14260-2900