Confluence theory for graphs

Sikora, Adam¹ ; Westbury, Bruce²

¹Department of Mathematics, SUNY Buffalo, Buffalo NY 14260, USA
²Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK

Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 439-478

Résumé

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.

Détail

DOI : 10.2140/agt.2007.7.439

Keywords: confluence, Diamond Lemma, spider, knot, link, skein

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