The Classification of S² × R 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 [7],[8]. One of these is S² × R, i.e. the direct product of the spherical plane S² and the real line R. Our purpose is the classification of the space groups of S² × R, i.e. discrete transformation groups which act on S² × R with a lattice on R (see section 3), analogously to that of the classical Euclidean geometry E³

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