Dynamics of compact homogeneous universes (Q2785755)

A complete description of the dynamics of compact locally homogeneous universes is given which, in particular, includes explicit calculations of Teichmüller deformations and careful counting of dynamical degrees of freedom. Each of the universes is regarded as a simply connected four-dimensional spacetime with identifications by the action of a discrete subgroup of the isometry group. One then reduces the section and finds a condition that such spatial identifications must satisfy. This is essential for the explicit construction of compact homogeneous universes. Some examples are demonstrated for Bianchi type II, \(\text{VI}_0\), \(\text{VII}_0\) and I universal covers.