Functional description of S1 x S2 and S3 Gowdy cosmologies

We will briefly review the classical formulation of the 3-handle S1 x S2 and 3-sphere S3 Gowdy cosmological models coupled with massless scalar fields and their exact (non-perturbative) quantization by defining suitable Schroedinger functional representations in terms of appropriate probability spaces. We will pay special attention to the construction of closed expressions for the corresponding quantum time evolution propagators.