2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/52099It is well-known that the sum over topologies in quantum gravity is ill-defined, due to a super-exponential growth of the number of geometries as a function of the space-time volume, leading to a badly divergent gravitational path integral. Not even in dimension 2, where a non-perturbative quantum gravity theory can be constructed explicitly from a (regularized) path integral, has this problem found a satisfactory solution. -- In the present work, we extend a previous 2d Lorentzian path integral, regulated in terms of Lorentzian random triangulations, to include space-times with an arbitrary number of handles. We show that after the imposition of physically motivated causality constraints, the combined sum over geometries and topologies is well-defined and possesses a continuum limit which yields a concrete model of space-time foam in two dimensions.13 pages, 6 Postscript figures; contribution to the proceedings of the Workshop on Random Geometry, Krakow, May 15-17, 2003High Energy Physics - Theorytext