SEIFERT MANIFOLDS WITH FIBER SPHERICAL SPACE-FORMS

We study the Seifert fiber spaces modeled on the product space S-3 x R (2). Such spaces are ''fiber bundles'' with singularities. The regular fibers are spherical space-forms of S-3, while singular fibers are fi nite quotients of regular fibers. For each of possible space-form grou ps Delta of S-3, We obtain a criterion for a group extension Pi of Del ta to act on S-3 x R(2) weakly S-3-equivariant maps, which gives rise to a Seifert fiber space modeled on S-3 x R(2) with weakly S-3-equivar iant maps TOPS3(S3 x R(2)) as the universal group. In the course of pr oving our main results, we also obtain an explicit formula for H-2(Q;Z ) for a compact crystallographic or Fuchsian group Q. Most of our meth ods for S-3 apply to compact Lie groups with discrete center, and we s tate some of our results in this general context.