On the Relevance of Singular Solutions in dS₃ and AdS₃ Gravity

Canonical quantization of three dimensional gravity in the first order formalism suggests that one should allow singular solutions. This paper addresses the importance of singular solutions in the path integral approach to quantum gravity. Using a simple ansatz for the dreibein and the spin connection in the de-Sitter and the anti-de-Sitter spaces we propose that the sum over the 3D manifolds in the path integral should be extended to include 2D surfaces.