Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Ponzano-Regge model   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.

17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio