2000/08/05 by Gaspare Carbone, Mauro Carfora, Annalisa Marzuoli · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Molecular spectroscopy and chirality #gr-qc
paper · pdf · doi:10.1016/s0550-3213(00)00729-x
published as Nucl.Phys.B619:654-688,2001 · 42 pages, 25 figures
arxiv created 2000/08/05 · openalex publication_date 2001/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In this paper we present classes of state sum models based on the recoupling theory of angular momenta of SU(2) (and of its q-counterpart Uq(sl(2)), q a root of unity). Such classes are arranged in hierarchies depending on the dimension d, and include all known closed models, i.e. the Ponzano-Regge state sum and the Turaev-Viro invariant in dimension d=3, the Crane-Yetter invariant in d=4. In general, the recoupling coefficient associated with a d-simplex turns out to be a \3(d-2)(d+1)/2\j symbol, or its q-analog. Each of the state sums can be further extended to compact triangulations (Td,∂ Td) of a PL-pair (Md,∂ Md), where the triangulation of the boundary manifold is not keeped fixed. In both cases we find out the algebraic identities which translate complete sets of topological moves, thus showing that all state sums are actually independent of the particular triangulation chosen. Then, owing to Pachner's theorems, it turns out that classes of PL-invariant models can be defined in any dimension d.