#### 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 $S{U}_{3}$–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