Volume 7, issue 1 (2007)

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

Volume 20, 1 issue

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

Author Index
The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
Other MSP Journals
Confluence theory for graphs

Adam S Sikora and Bruce W Westbury

Algebraic & Geometric Topology 7 (2007) 439–478

arXiv: math.QA/0609832


We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie algebra of rank at most 2, gives rise to a confluent system of reduction rules of graphs (via Kuperberg’s spiders) in an arbitrary surface. As a further consequence of this result, we find canonical bases of SU3–skein modules of cylinders over orientable surfaces.

confluence, Diamond Lemma, spider, knot, link, skein
Mathematical Subject Classification 2000
Primary: 57M15, 57M27
Secondary: 05C10, 16S15
Received: 9 October 2006
Accepted: 12 January 2007
Published: 25 April 2007
Adam S Sikora
Department of Mathematics
SUNY Buffalo
Buffalo NY 14260
Bruce W Westbury
Mathematics Institute
University of Warwick