In a quantum gravity scenario, new questions can be tackled such as, for instance, the posibility of quantum transition of topology. As it is well known, classical transtions of topology are incompatible withe causality and regularity principles. We intend to exhibit quantum transitions of topology in the primordial Universe and examine the possibility of quantum fluctuations of topology in a family of black holes.

Nelson Pinto Neto, Jerôme Martin, Vitório A. De Lorenci e I.D.Soares have been studying quantum transitons of topology, and have obtained approximate Green?s functions describing such transitions and obtaining selection rules.