2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57961We describe some results concerning the phase space of 3-dimensional Einstein gravity when space is a torus and with negative cosmological constant. The approach uses the holonomy matrices of flat SL(2,R) connections on the torus to parametrise the geometry. After quantization, these matrices acquire non-commuting entries, in such a way that they satisfy q-commutation relations and exhibit interesting geometrical properties. In particular they lead to a quantization of the Goldman bracket.12 pages, including contents page (proceedings format), submitted to the Proceedings of the XIII Fall Workshop on Geometry and Physics, Murcia, Sept. 20-22, 2004Mathematical Physics83C45text