- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:39
Quantum Topology
Quantum Topol.
QT
1663-487X
1664-073X
General
10.4171/QT
http://www.ems-ph.org/doi/10.4171/QT
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
5
2014
2
Integrality of Kauffman brackets of trivalent graphs
Francesco
Costantino
Université Paul Sabatier, TOULOUSE, FRANCE
Spin networks, quantum invariants, Jones polynomials, trivalent graphs
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 $R$-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 $6j$-symbols of $U_q(\operatorname{sl}_2)$.
Manifolds and cell complexes
General
143
184
10.4171/QT/49
http://www.ems-ph.org/doi/10.4171/QT/49