Confluence theory for graphs

Sikora, Adam; Westbury, Bruce

doi:10.2140/agt.2007.7.439

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Confluence theory for graphs

Adam S Sikora and Bruce W Westbury

Algebraic & Geometric Topology 7 (2007) 439–478

DOI: 10.2140/agt.2007.7.439

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

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/

Volume 7, issue 1 (2007)