Volume 7, issue 1 (2007)

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Confluence theory for graphs

Adam S Sikora and Bruce W Westbury

Algebraic & Geometric Topology 7 (2007) 439–478

arXiv: math.QA/0609832

Abstract

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.

Keywords
confluence, Diamond Lemma, spider, knot, link, skein
Mathematical Subject Classification 2000
Primary: 57M15, 57M27
Secondary: 05C10, 16S15
References
Publication
Received: 9 October 2006
Accepted: 12 January 2007
Published: 25 April 2007
Authors
Adam S Sikora
Department of Mathematics
SUNY Buffalo
Buffalo NY 14260
USA
http://www.math.buffalo.edu/~asikora/
Bruce W Westbury
Mathematics Institute
University of Warwick
Coventry
CV4 7AL
UK
http://www.maths.warwick.ac.uk/~bww/