Confluence Theory for Graphs

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 SU_3-skein modules of cylinders over orientable surfaces.

34 pages, 218 figures

References in corpus (2)

• Skein theory for SU(n)-quantum invariants
• Invariant tensors for the spin representation of so(7)

Cited by in corpus (19)

• Skein theory for the D_{2n} planar algebras
• A Diagrammatic Category for the Representation Theory of U_q(sl_n)
• Quantum Teichmüller spaces and quantum trace map
• Invariant tensors for the spin representation of so(7)
• The Localized Skein Algebra is Frobenius
• Double affine Hecke algebras and generalized Jones polynomials
• Skein and cluster algebras of unpunctured surfaces for ${\mathfrak{sl}}_3$
• Frobenius Algebras Derived from the Kauffman Bracket Skein Algebra
• Triangular decomposition of $S{L}_3$ skein algebras
• Adequate links in thickened surfaces and the generalized Tait conjectures
• Iterated torus knots and double affine Hecke algebras
• Tropical Fock-Goncharov coordinates for ${\mathrm{SL}}_3$-webs on surfaces I: construction
• Naturality of ${\mathrm{SL}}_3$ quantum trace maps for surfaces
• Verification Of The Jones Unknot Conjecture Up To 24 Crossings
• Tropical Fock-Goncharov coordinates for ${\mathrm{SL}}_3$-webs on surfaces II: naturality
• Power sum elements in the $G_2$ skein algebra
• Verification Of The Jones Unknot Conjecture Up To 23 Crossings
• The zero stability for the one-row colored ${\mathfrak{sl}}_3$ Jones polynomial
• Generating sets for the Kauffman skein module of a family of Seifert fibered spaces