The classification of S²xR space groups

Abstract

The geometrization of 3-manifolds plays an important role in various topological investigations and in the geometry as well. Thurston classified the eight simply connected 3-dimensional maximal homogeneous Riemannian geometries. One of these is S^2xR, i.e. the direct product of the spherical plane S^2 and the real line R. Our purpose is the classification of the space groups of S^2xR, i.e. discrete transformation groups which act on S^2xR with a lattice on R (see section 3), analogously to that of the classical Euclidean geometry E^3.