Integrality of Kauffman brackets of trivalent graphs

  • Francesco Costantino

    Université Paul Sabatier, Toulouse, France


We show that Kauffman brackets of colored framed graphs (also known as quantum spin networks) can be renormalized to a Laurent polynomial with integer coefficients by multiplying it by a coefficient which is a product of quantum factorials depending only on the abstract combinatorial structure of the graph. Then we compare the shadow-state sums and the state-sums based on -matrices and Clebsch–Gordan symbols, reprove their equivalence and comment on the integrality of the weight of the states. We also provide short proofs of most of the standard identities satisfied by quantum -symbols of .

Cite this article

Francesco Costantino, Integrality of Kauffman brackets of trivalent graphs. Quantum Topol. 5 (2014), no. 2, pp. 143–184

DOI 10.4171/QT/49