@article{barrett_naish-guzman_2009, 
  title={The Ponzano-Regge model}, 
  abstractNote={The definition of the Ponzano-Regge state-sum model of three-dimensional
quantum gravity with a class of local observables is developed. The main
definition of the Ponzano-Regge model in this paper is determined by its
reformulation in terms of group variables. The regularisation is defined and a
proof is given that the partition function is well-defined only when a certain
cohomological criterion is satisfied. In that case, the partition function may
be expressed in terms of a topological invariant, the Reidemeister torsion.
This proves the independence of our definition on the triangulation of the
3-manifold and on those arbitrary choices made in the regularisation. A further
corollary is that when the observable is a knot, the partition function (when
it exists) can be written in terms of the Alexander polynomial of the knot.
Various examples of observables in the three-sphere are computed explicitly.
Alternative regularisations of the Ponzano-Regge model by the simple cutoff
procedure and by the limit of the Turaev-Viro model are discussed, giving
successes and limitations of these approaches.}, 
  author={Barrett and Naish-Guzman}, 
  year={2009}, 
  month={Mar}
  }