DYNAMICS OF COMPACT HOMOGENEOUS UNIVERSES

A complete description of dynamics of compact locally homogeneous univ erses is given, which, in particular, includes explicit calculations o f Teichmuller deformations and careful counting of dynamical degrees o f freedom, We regard each of the universes as a simply connected four- dimensional space-time with identifications by the action of a discret e subgroup of the isometry group. We then reduce the identifications d efined by the space-time isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. T his is essential for explicit construction of compact homogeneous univ erses. Some examples are demonstrated for Bianchi II, VI0, VII0, and I universal covers. (C) 1997 American Institute of Physics.