Florian Girelli et al 2002 Class. Quantum Grav. 19 1093 doi:10.1088/0264-9381/19/6/305
Florian Girelli1,2, Robert Oeckl1 and Alejandro Perez1,3
Show affiliationsWe provide a simple proof of the topological invariance of the Turaev–Viro model (corresponding to simplicial 3D pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our results extend to a vast class of quantum groups. The techniques introduced here could be relevant for investigating the scaling properties of non-topological state sums, proposed as models of quantum gravity in 4D, under refinement of the cellular decomposition.
57R56 Topological quantum field theories
Issue 6 (21 March 2002)
Received 26 November 2001, in final form 10 January 2002
Published 25 February 2002
Florian Girelli et al 2002 Class. Quantum Grav. 19 1093
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