2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35089We provide a mathematical definition of the gauge fixed Ponzano-Regge model showing that it gives a measure on the space of flat connections whose volume is well defined. We then show that the Ponzano-Regge model can be equivalently expressed as Reshetikhin-Turaev evaluation of a colored chain mail link based on D(SU(2)): a non compact quantum group being the Drinfeld double of SU(2) and a deformation of the Poincare algebra. This proves the equivalence between spin foam quantization and Chern-Simons quantization of three dimensional gravity without cosmological constant. We extend this correspondence to the computation of expectation value of physical observables and insertion of particles.27 + 23 pages, many figuresGeneral Relativity and Quantum CosmologyHigh Energy Physics - TheoryQuantum Algebratext