2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51042After briefly reviewing the hamiltonian approach to 2+1 dimensional gravity in absence of matter on closed universes, we consider 2+1 dimensional gravity coupled to point particles in an open universe. We show that the hamiltonian structure of the theory is the result of a conjecture put forward by Polyakov in a different context. A proof is given of such a conjecture. Finally we give the exact quantization of the two particle problem in open space.Talk by P. Menotti at the 25th Johns Hopkins Workshop, Florence September 3-5, 2001, 14 pages LaTexHigh Energy Physics - Theorytext