Confluence theory for graphs
Copyright policy )Confluence theory for graphs
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 SU_3-skein modules of cylinders over orientable surfaces.
34 pages, 218 figures
- University at Buffalo, State University of New York United States
- University of Warwick United Kingdom
- SUNY at Buffalo United States
57M15, 57M27, 05C10, 16S15, link, Geometric Topology (math.GT), Invariants of knots and \(3\)-manifolds, Enumeration in graph theory, Planar graphs; geometric and topological aspects of graph theory, Mathematics - Geometric Topology, 16S15, 57M27, 57M15, knot, confluence, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Relations of low-dimensional topology with graph theory, Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting), skein, Simple, semisimple, reductive (super)algebras, spider, Diamond Lemma, 05C10, diamond Lemma
57M15, 57M27, 05C10, 16S15, link, Geometric Topology (math.GT), Invariants of knots and \(3\)-manifolds, Enumeration in graph theory, Planar graphs; geometric and topological aspects of graph theory, Mathematics - Geometric Topology, 16S15, 57M27, 57M15, knot, confluence, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Relations of low-dimensional topology with graph theory, Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting), skein, Simple, semisimple, reductive (super)algebras, spider, Diamond Lemma, 05C10, diamond Lemma
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