Bianchi cosmologies: the role of spatial topology

The role of spatial topology in the Hamiltonian description of Bianchi models is analysed. It turns out that, in general, the number of degrees of freedom of these models is not uniquely determined by the isometry group but depends in addition on the choice of topology. Consequently, the quantum theory is quite sensitive to this choice. Contrary to one's initial expectation, subtleties arise in the spatially open models-say with topology R3-rather than closed. Finally, it is shown that class B models cannot occur with closed topologies.