On Spectral Triples in Quantum Gravity II
  A semifinite spectral triple for an algebra canonically associated to canonical quantum gravity is constructed. The algebra is generated by based loops in a triangulation and its barycentric subdivisions. The underlying space can be seen as a gauge fixing of the unconstrained state space of Loop Quantum Gravity. This paper is the second of two papers on the subject. 
Johannes Aastrup, Jesper M. Grimstrup, Ryszard Nest