Topological quantum field theory and polynomial identities for graphs on the torus

DOI10.4171/aihpd/130zbMath1530.57009arXiv1902.02760MaRDI QIDQ6100161

Vyacheslav S. Krushkal, Paul Fendley

Publication date: 11 May 2023

Published in: Annales de l'Institut Henri Poincaré D. Combinatorics, Physics and their Interactions (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.02760

zbMATH Keywords

graphs on surfacestopological quantum field theoryTutte golden identitytopological Tutte polynomial

Mathematics Subject Classification ID

Graph polynomials (05C31) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Topological quantum field theories (aspects of differential topology) (57R56) Relations of low-dimensional topology with graph theory (57M15) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16)

Cites Work

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• Knot polynomial identities and quantum group coincidences
• Link invariants, the chromatic polynomial and the Potts model
• A polynomial of graphs on surfaces
• Tutte chromatic identities from the Temperley-Lieb algebra
• Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models
• Topological quantum field theories derived from the Kauffman bracket
• Topological graph polynomials and quantum field theory. I: Theory kernel theories
• Tutte relations, TQFT, and planarity of cubic graphs
• Dimers on surface graphs and spin structures. I
• The Jones polynomial and graphs on surfaces
• Wagner's theorem for torus graphs
• Bemerkungen zum Vierfarbenproblem
• Topological defects on the lattice: I. The Ising model
• Graphs, Links, and Duality on Surfaces
• Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134)
• Asymptotics of quantum representations of surface groups
• Structure of the flow and Yamada polynomials of cubic graphs
• Planar diagrams for local invariants of graphs in surfaces
• On chromatic polynomials and the golden ratio
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
• Diagonal flips in pseudo-triangulations on closed surfaces

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