Wigner symbols and combinatorial invariants of three-manifolds with boundary
type: Item
instance of: scholarly article
title: Wigner symbols and combinatorial invariants of three-manifolds with boundary
zbMATH Open document ID: 0959.57006
DOI: 10.1007/PL00005527
author: Gaspare Carbone
author: Mauro Carfora
author: Annalisa Marzuoli
published in: Communications in Mathematical Physics
publication date: 2001-04-29T00:00:00Z
review text: The authors extend both the Ponzano-Regge function and the Turaev-Viro invariant to compact 3-dimensional simplicial PL-manifolds with non-empty boundaries. In their approach the presence of a 2-dimensional boundary is taken into account through the introduction in the state sum \(Z[(M, \partial M)]\) of a Wigner \(3jm\) symbol associated with each triangle lying in the boundary itself. The results established for the classical SU(2)-invariant \(Z[(M, \partial M)]\) are extended to the case of the quantized enveloping algebra \(U_q(sl(2,C))\) (\(q\) a root of unit). The resulting quantum invariant \(Z_q[(M, \partial M)]\) is the counterpart of the Turaev-Viro invariant for a closed 3-dimensional PL-manifold.
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 81S30
Mathematics Subject Classification ID: 57N10
zbMATH DE Number: 1523445
zbMATH Keywords: 3-manifold invariants
reviewed by: A. K. Guts
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1523445