The classification of S²xR space groups

Citation

Farkas JZ (2001) The classification of S²xR space groups. Beitrage zur Algebra und Geometrie / Contributions to Algebra and Geometry, 42 (1), pp. 235-250. http://www.emis.de/journals/BAG/vol.42/no.1/15.html

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.

Keywords
Thurston-geometries; crystallographic groups

Notes
The full text version of this work is available from the journal web pages: http://www.emis.de/journals/BAG/vol.42/no.1/15.html.

Journal
Beitrage zur Algebra und Geometrie / Contributions to Algebra and Geometry: Volume 42, Issue 1