Polynomial 6j-Symbols and States Sums - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Algebraic and Geometric Topology Année : 2011

Polynomial 6j-Symbols and States Sums

Résumé

For q a root of unity of order 2r, we give explicit formulas of a family of 3-variable Laurent polynomials J_{i,j,k} with coefficients in Z[q] that encode the 6j-symbols associated with nilpotent representations of U_qsl_2. For a given abelian group G, we use them to produce a state sum invariant tau^r(M,L,h_1,h_2) of a quadruplet (compact 3-manifold M, link L inside M, homology class h_1\in H_1(M,Z), homology class h_2\in H_2(M,G)) with values in a ring R related to G. The formulas are established by a ''skein'' calculus as an application of the theory of modified dimensions introduced in [arXiv:0711.4229]. For an oriented 3-manifold M, the invariants are related to TV(M,L,f\in H^1(M,C^*)) defined in [arXiv:0910.1624] from the category of nilpotent representations of U_qsl_2. They refine them as TV(M,L,f)= Sum_h tau^r(M,L,h,f') where f' correspond to f with the isomorphism H_2(M,C^*) ~ H^1(M,C^*).

Dates et versions

hal-00520476 , version 1 (23-09-2010)

Identifiants

Citer

Nathan Geer, Bertrand Patureau-Mirand. Polynomial 6j-Symbols and States Sums. Algebraic and Geometric Topology, 2011, pp.11 (2011) 1821--1860. ⟨10.2140/agt.2011.11.1821⟩. ⟨hal-00520476⟩
77 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More